Roboguru

Hasil dari 24​(8​−23​)+2​24​ adalah ....

Pertanyaan

Hasil dari square root of 24 open parentheses square root of 8 minus 2 square root of 3 close parentheses plus fraction numerator 24 over denominator square root of 2 end fraction adalah ....

  1. 8 square root of 2 plus 12 square root of 3

  2. 8 square root of 3 minus 12 square root of 3

  3. 8 square root of 2

  4. 8 square root of 3

Pembahasan Video:

Pembahasan Soal:

Ingat : rightwards double arrow square root of a cross times square root of b equals square root of a cross times b end root rightwards double arrow a square root of b plus-or-minus c square root of b equals open parentheses a plus-or-minus c close parentheses square root of b

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 24 open parentheses square root of 8 minus 2 square root of 3 close parentheses plus fraction numerator 24 over denominator square root of 2 end fraction end cell equals cell square root of 192 minus 2 square root of 72 plus fraction numerator 24 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell square root of 64 cross times 3 end root minus 2 square root of 36 cross times 2 end root plus 24 over 2 square root of 2 end cell row blank equals cell 8 square root of 3 minus 12 square root of 2 plus 12 square root of 2 end cell row blank equals cell 8 square root of 3 end cell end table

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 07 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika b=a3 dan c=a23​, maka hasil dari 45a6​+20b2​−5c4​ adalah ....

Pembahasan Soal:

Perhatikan bahwa

begin mathsize 14px style square root of 45 a to the power of 6 end root plus square root of 20 b squared end root minus square root of 5 c to the power of 4 end root equals square root of 9 a to the power of 6 times 5 end root plus square root of 4 b squared times 5 end root minus square root of 5 c to the power of 4 end root equals 3 a cubed square root of 5 plus 2 b square root of 5 minus c squared square root of 5 equals open parentheses 3 a cubed plus 2 b minus c squared close parentheses square root of 5 end style   

Diketahui bahwa undefined dan undefined, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 a cubed plus 2 b minus c squared close parentheses square root of 5 end cell equals cell open parentheses 3 a cubed plus 2 open parentheses a cubed close parentheses minus open parentheses a to the power of 3 over 2 end exponent close parentheses squared close parentheses square root of 5 end cell row blank equals cell open parentheses 3 a cubed plus 2 a cubed minus a cubed close parentheses square root of 5 end cell row blank equals cell open parentheses 3 plus 2 minus 1 close parentheses a cubed square root of 5 end cell row blank equals cell 4 a cubed square root of 5 end cell end table end style 

 Dengan demikian hasil dari undefined adalah undefined.

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Rasionalkan penyebut pecahan-pecachan berikut! 8​3​−4​

Pembahasan Soal:

Ingat kembali aturan berikut. 

  • square root of a cross times square root of b equals square root of a cross times b end root 
  • Bentuk akar fraction numerator square root of a over denominator square root of b end fraction dapat dirasionalkan dengan cara fraction numerator square root of a over denominator square root of b end fraction cross times fraction numerator square root of b over denominator square root of b end fraction 
  • open parentheses a minus b close parentheses cross times square root of c equals a cross times square root of c minus b cross times square root of c 
  • p square root of a plus p square root of b equals p open parentheses square root of a plus square root of b close parentheses 

Dari rumus di atas, diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction end cell equals cell fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction cross times fraction numerator square root of 8 over denominator square root of 8 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 3 minus 4 close parentheses cross times square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 3 cross times square root of 8 minus 4 cross times square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 3 cross times 8 end root minus 4 square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 24 minus 4 square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 2 squared cross times 6 end root minus 4 square root of 2 squared cross times 2 end root over denominator 8 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 4 cross times 2 square root of 2 over denominator 8 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 8 square root of 2 over denominator 8 end fraction end cell row blank equals cell fraction numerator up diagonal strike 2 to the power of 1 cross times open parentheses square root of 6 minus 4 square root of 2 close parentheses over denominator up diagonal strike 8 to the power of 4 end fraction end cell row blank equals cell fraction numerator square root of 6 minus 4 square root of 2 over denominator 4 end fraction end cell end table 

Jadi, hasil dari merasionalkan fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 6 minus 4 square root of 2 over denominator 4 end fraction end cell end table.

0

Roboguru

Misalkan a=22​−8−42​​ dan b=22​+8−42​​. Jika ba​+ab​=x+y2​ dengan x,y  bulat, maka nilai x+y adalah...

Pembahasan Soal:

Bentuk akar yang sejenis (memiliki bilangan pokok dan akar pangkat sama) dapat ditambahkan atau dikurangkan. Caranya adalah menambah atau mengurang bilangan yang didepan bentuk akar tersebut seperti berikut.

p square root of x plus q square root of x equals open parentheses p plus q close parentheses square root of x p square root of x minus q square root of x equals open parentheses p minus q close parentheses square root of x

Pada soal diketahui a over b plus b over a equals x plus y square root of 2, selesaikan ruas kiri terlebih dahulu:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a over b plus b over a end cell row blank equals cell fraction numerator a squared plus b squared over denominator a b end fraction end cell row blank equals cell fraction numerator open parentheses 2 square root of 2 minus square root of 8 minus 4 square root of 2 end root close parentheses squared plus open parentheses 2 square root of 2 plus square root of 8 minus 4 square root of 2 end root close parentheses squared over denominator open parentheses 2 square root of 2 minus square root of 8 minus 4 square root of 2 end root close parentheses open parentheses 2 square root of 2 plus square root of 8 minus 4 square root of 2 end root close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 2 square root of 2 close parentheses squared up diagonal strike negative 4 square root of 2 open parentheses square root of 8 minus 4 square root of 2 end root close parentheses end strike plus open parentheses square root of 8 minus 4 square root of 2 end root close parentheses squared plus open parentheses 2 square root of 2 close parentheses squared up diagonal strike plus 4 square root of 2 open parentheses square root of 8 minus 4 square root of 2 end root close parentheses end strike plus open parentheses square root of 8 minus 4 square root of 2 end root close parentheses squared over denominator open parentheses 2 square root of 2 close parentheses squared minus open parentheses square root of 8 minus 4 square root of 2 end root close parentheses squared end fraction end cell row blank equals cell fraction numerator 8 plus 8 minus 4 square root of 2 plus 8 plus 8 minus 4 square root of 2 over denominator 8 minus open parentheses 8 minus 4 square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator 32 minus 8 square root of 2 over denominator 4 square root of 2 end fraction end cell row blank equals cell fraction numerator 8 minus 2 square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 8 minus 2 square root of 2 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 8 square root of 2 minus 4 over denominator 2 end fraction end cell row blank equals cell 4 square root of 2 minus 2 end cell end table

Karena a over b plus b over a equals x plus y square root of 2, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell a over b plus b over a end cell equals cell x plus y square root of 2 end cell row cell 4 square root of 2 minus 2 end cell equals cell x plus y square root of 2 end cell row cell negative 2 plus 4 square root of 2 end cell equals cell x plus y square root of 2 end cell end table

Dari persamaan di atas, maka nilai x equals negative 2 dan y equals 4.

Ditanyakan nilai dari x plus y yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals cell negative 2 plus 4 end cell row blank equals 2 end table

Dengan demikian, telah diperoleh nilai dari x plus y yaitu 2.

0

Roboguru

Diketahui a=7​+5​ dan b=7​−5​. Nilai dari a+bab​ adalah ....

Pembahasan Soal:

Diketahui begin mathsize 14px style a equals square root of 7 plus square root of 5 end style dan begin mathsize 14px style b equals square root of 7 minus square root of 5 end style maka begin mathsize 14px style fraction numerator a b over denominator a plus b end fraction end style diperoleh sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a b over denominator a plus b end fraction end cell equals cell fraction numerator open parentheses square root of 7 plus square root of 5 close parentheses open parentheses square root of 7 minus square root of 5 close parentheses over denominator open parentheses square root of 7 plus square root of 5 close parentheses plus open parentheses square root of 7 minus square root of 5 close parentheses end fraction end cell row blank equals cell fraction numerator 7 minus 5 over denominator 2 square root of 7 end fraction end cell row blank equals cell fraction numerator 2 over denominator 2 square root of 7 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 7 end fraction times fraction numerator square root of 7 over denominator square root of 7 end fraction end cell row blank equals cell 1 over 7 square root of 7 end cell end table end style

Jadi nilai dari begin mathsize 14px style fraction numerator a b over denominator a plus b end fraction end style adalah begin mathsize 14px style 1 over 7 square root of 7 end style.

Oleh karena itu jawaban yang tepat adalah B.

0

Roboguru

Rasionalkan penyebut pecahan-pecahan berikut! e. 12​−35​ f. 7​+6​63​​ g. 15​−8​4+5​​ h. 43​+6​8​−2​​

Pembahasan Soal:

e. Diketahui fraction numerator 5 over denominator square root of 12 minus 3 end fraction maka cara untuk merasionalkannya adalah dengan mengalikan akar sekawan dari square root of 12 minus 3 yaitu square root of 12 plus 3 sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 over denominator square root of 12 minus 3 end fraction end cell equals cell fraction numerator 5 over denominator square root of 12 minus 3 end fraction cross times fraction numerator square root of 12 plus 3 over denominator square root of 12 plus 3 end fraction end cell row blank equals cell fraction numerator 5 open parentheses square root of 12 plus 3 close parentheses over denominator open parentheses square root of 12 minus 3 close parentheses open parentheses square root of 12 plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 5 cross times square root of 12 plus 5 cross times 3 over denominator square root of 12 cross times square root of 12 plus 3 cross times square root of 12 minus 3 cross times square root of 12 minus 3 cross times 3 end fraction end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 over denominator square root of 12 minus 3 end fraction end cell equals cell fraction numerator 5 over denominator square root of 12 minus 3 end fraction cross times fraction numerator square root of 12 plus 3 over denominator square root of 12 plus 3 end fraction end cell row blank equals cell fraction numerator 5 open parentheses square root of 12 plus 3 close parentheses over denominator open parentheses square root of 12 minus 3 close parentheses open parentheses square root of 12 plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 5 cross times square root of 12 plus 5 cross times 3 over denominator square root of 12 cross times square root of 12 plus 3 cross times square root of 12 minus 3 cross times square root of 12 minus 3 cross times 3 end fraction end cell row blank equals cell fraction numerator 5 square root of 12 plus 15 over denominator square root of 12 cross times 12 end root plus up diagonal strike 3 square root of 12 minus 3 square root of 12 end strike minus 9 end fraction end cell row blank equals cell fraction numerator 5 square root of 12 plus 15 over denominator square root of 12 squared end root minus 9 end fraction end cell row blank equals cell fraction numerator 5 square root of 12 plus 15 over denominator 12 minus 9 end fraction end cell row blank equals cell fraction numerator 5 square root of 12 plus 15 over denominator 3 end fraction end cell end table

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 over denominator square root of 12 minus 3 end fraction end cell equals cell fraction numerator 5 over denominator square root of 12 minus 3 end fraction cross times fraction numerator square root of 12 plus 3 over denominator square root of 12 plus 3 end fraction end cell row blank equals cell fraction numerator 5 open parentheses square root of 12 plus 3 close parentheses over denominator open parentheses square root of 12 minus 3 close parentheses open parentheses square root of 12 plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 5 cross times square root of 12 plus 5 cross times 3 over denominator square root of 12 cross times square root of 12 plus 3 cross times square root of 12 minus 3 cross times square root of 12 minus 3 cross times 3 end fraction end cell row blank equals cell fraction numerator 5 square root of 12 plus 15 over denominator square root of 12 cross times 12 end root plus up diagonal strike 3 square root of 12 minus 3 square root of 12 end strike minus 9 end fraction end cell row blank equals cell fraction numerator 5 square root of 12 plus 15 over denominator square root of 12 squared end root minus 9 end fraction end cell row blank equals cell fraction numerator 5 square root of 12 plus 15 over denominator 12 minus 9 end fraction end cell row blank equals cell fraction numerator 5 square root of 12 plus 15 over denominator 3 end fraction end cell row blank equals cell fraction numerator 5 square root of 4 cross times 3 end root plus 15 over denominator 3 end fraction end cell row blank equals cell fraction numerator 5 square root of 2 squared cross times 3 end root plus 15 over denominator 3 end fraction end cell row blank equals cell fraction numerator 5 cross times 2 square root of 3 plus 15 over denominator 3 end fraction end cell row blank equals cell fraction numerator 10 square root of 3 plus 15 over denominator 3 end fraction end cell end table

Jadi bentuk rasional dari fraction numerator 5 over denominator square root of 12 minus 3 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 10 square root of 3 plus 15 over denominator 3 end fraction end cell end table.

f. Diketahui fraction numerator 6 square root of 3 over denominator square root of 7 plus square root of 6 end fraction maka cara merasionalkannya adalah dengan mengalikan penyebut akar dengan akar sekawannya yaitu square root of 7 minus square root of 6 sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 square root of 3 over denominator square root of 7 plus square root of 6 end fraction end cell equals cell fraction numerator 6 square root of 3 over denominator square root of 7 plus square root of 6 end fraction cross times fraction numerator square root of 7 minus square root of 6 over denominator square root of 7 minus square root of 6 end fraction end cell row blank equals cell fraction numerator 6 square root of 3 open parentheses square root of 7 minus square root of 6 close parentheses over denominator open parentheses square root of 7 plus square root of 6 close parentheses open parentheses square root of 7 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator 6 square root of 3 cross times square root of 7 minus 6 square root of 3 cross times square root of 6 over denominator square root of 7 cross times square root of 7 minus square root of 7 cross times square root of 6 plus square root of 6 cross times square root of 7 minus square root of 6 cross times square root of 6 end fraction end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 square root of 3 over denominator square root of 7 plus square root of 6 end fraction end cell equals cell fraction numerator 6 square root of 3 over denominator square root of 7 plus square root of 6 end fraction cross times fraction numerator square root of 7 minus square root of 6 over denominator square root of 7 minus square root of 6 end fraction end cell row blank equals cell fraction numerator 6 square root of 3 open parentheses square root of 7 minus square root of 6 close parentheses over denominator open parentheses square root of 7 plus square root of 6 close parentheses open parentheses square root of 7 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator 6 square root of 3 cross times square root of 7 minus 6 square root of 3 cross times square root of 6 over denominator square root of 7 cross times square root of 7 minus square root of 7 cross times square root of 6 plus square root of 6 cross times square root of 7 minus square root of 6 cross times square root of 6 end fraction end cell row blank equals cell fraction numerator 6 square root of 3 cross times 7 end root minus 6 square root of 3 cross times 6 end root over denominator square root of 7 cross times 7 end root minus square root of 7 cross times 6 end root plus square root of 6 cross times 7 end root minus square root of 6 cross times 6 end root end fraction end cell row blank equals cell fraction numerator 6 square root of 21 minus 6 square root of 18 over denominator square root of 49 up diagonal strike negative square root of 42 plus square root of 42 end strike minus square root of 36 end fraction end cell row blank equals cell fraction numerator 6 square root of 21 minus 6 square root of 18 over denominator square root of 49 minus square root of 36 end fraction end cell end table

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 square root of 3 over denominator square root of 7 plus square root of 6 end fraction end cell equals cell fraction numerator 6 square root of 3 over denominator square root of 7 plus square root of 6 end fraction cross times fraction numerator square root of 7 minus square root of 6 over denominator square root of 7 minus square root of 6 end fraction end cell row blank equals cell fraction numerator 6 square root of 3 open parentheses square root of 7 minus square root of 6 close parentheses over denominator open parentheses square root of 7 plus square root of 6 close parentheses open parentheses square root of 7 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator 6 square root of 3 cross times square root of 7 minus 6 square root of 3 cross times square root of 6 over denominator square root of 7 cross times square root of 7 minus square root of 7 cross times square root of 6 plus square root of 6 cross times square root of 7 minus square root of 6 cross times square root of 6 end fraction end cell row blank equals cell fraction numerator 6 square root of 3 cross times 7 end root minus 6 square root of 3 cross times 6 end root over denominator square root of 7 cross times 7 end root minus square root of 7 cross times 6 end root plus square root of 6 cross times 7 end root minus square root of 6 cross times 6 end root end fraction end cell row blank equals cell fraction numerator 6 square root of 21 minus 6 square root of 18 over denominator square root of 49 up diagonal strike negative square root of 42 plus square root of 42 end strike minus square root of 36 end fraction end cell row blank equals cell fraction numerator 6 square root of 21 minus 6 square root of 18 over denominator square root of 49 minus square root of 36 end fraction end cell row blank equals cell fraction numerator 6 square root of 21 minus 6 square root of 9 cross times 2 end root over denominator 7 minus 6 end fraction end cell row blank equals cell fraction numerator 6 square root of 21 minus 6 square root of 3 squared cross times 2 end root over denominator 1 end fraction end cell row blank equals cell 6 square root of 21 minus 6 cross times 3 square root of 2 end cell row blank equals cell 6 square root of 21 minus 18 square root of 2 end cell end table

Jadi bentuk rasional dari fraction numerator 6 square root of 3 over denominator square root of 7 plus square root of 6 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 square root of 21 minus 18 square root of 2 end cell end table.

g. Diketahui fraction numerator 4 plus square root of 5 over denominator square root of 15 minus square root of 8 end fraction maka cara merasionalkannya adalah dengan mengalikan penyebut dengan akar sekawannya yaitu square root of 15 plus square root of 8 sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 4 plus square root of 5 over denominator square root of 15 minus square root of 8 end fraction end cell equals cell fraction numerator 4 plus square root of 5 over denominator square root of 15 minus square root of 8 end fraction cross times fraction numerator square root of 15 plus square root of 8 over denominator square root of 15 plus square root of 8 end fraction end cell row blank equals cell fraction numerator open parentheses 4 plus square root of 5 close parentheses open parentheses square root of 15 plus square root of 8 close parentheses over denominator open parentheses square root of 15 minus square root of 8 close parentheses open parentheses square root of 15 plus square root of 8 close parentheses end fraction end cell row blank equals cell fraction numerator 4 cross times square root of 15 plus 4 cross times square root of 8 plus square root of 5 cross times square root of 15 plus square root of 5 cross times square root of 8 over denominator square root of 15 cross times square root of 15 plus square root of 15 cross times square root of 8 minus square root of 8 cross times square root of 15 minus square root of 8 cross times square root of 8 end fraction end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 4 plus square root of 5 over denominator square root of 15 minus square root of 8 end fraction end cell equals cell fraction numerator 4 plus square root of 5 over denominator square root of 15 minus square root of 8 end fraction cross times fraction numerator square root of 15 plus square root of 8 over denominator square root of 15 plus square root of 8 end fraction end cell row blank equals cell fraction numerator open parentheses 4 plus square root of 5 close parentheses open parentheses square root of 15 plus square root of 8 close parentheses over denominator open parentheses square root of 15 minus square root of 8 close parentheses open parentheses square root of 15 plus square root of 8 close parentheses end fraction end cell row blank equals cell fraction numerator 4 cross times square root of 15 plus 4 cross times square root of 8 plus square root of 5 cross times square root of 15 plus square root of 5 cross times square root of 8 over denominator square root of 15 cross times square root of 15 plus square root of 15 cross times square root of 8 minus square root of 8 cross times square root of 15 minus square root of 8 cross times square root of 8 end fraction end cell row blank equals cell fraction numerator 4 square root of 15 plus 4 square root of 8 plus square root of 5 cross times 15 end root plus square root of 5 cross times 8 end root over denominator square root of 15 cross times 15 end root plus square root of 15 cross times 8 end root minus square root of 8 cross times 15 end root minus square root of 8 cross times 8 end root end fraction end cell row blank equals cell fraction numerator 4 square root of 15 plus 4 square root of 8 plus square root of 75 plus square root of 40 over denominator square root of 15 squared end root plus square root of 120 minus square root of 120 minus square root of 64 end fraction end cell end table

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 4 plus square root of 5 over denominator square root of 15 minus square root of 8 end fraction end cell equals cell fraction numerator 4 plus square root of 5 over denominator square root of 15 minus square root of 8 end fraction cross times fraction numerator square root of 15 plus square root of 8 over denominator square root of 15 plus square root of 8 end fraction end cell row blank equals cell fraction numerator open parentheses 4 plus square root of 5 close parentheses open parentheses square root of 15 plus square root of 8 close parentheses over denominator open parentheses square root of 15 minus square root of 8 close parentheses open parentheses square root of 15 plus square root of 8 close parentheses end fraction end cell row blank equals cell fraction numerator 4 cross times square root of 15 plus 4 cross times square root of 8 plus square root of 5 cross times square root of 15 plus square root of 5 cross times square root of 8 over denominator square root of 15 cross times square root of 15 plus square root of 15 cross times square root of 8 minus square root of 8 cross times square root of 15 minus square root of 8 cross times square root of 8 end fraction end cell row blank equals cell fraction numerator 4 square root of 15 plus 4 square root of 8 plus square root of 5 cross times 15 end root plus square root of 5 cross times 8 end root over denominator square root of 15 cross times 15 end root plus square root of 15 cross times 8 end root minus square root of 8 cross times 15 end root minus square root of 8 cross times 8 end root end fraction end cell row blank equals cell fraction numerator 4 square root of 15 plus 4 square root of 8 plus square root of 75 plus square root of 40 over denominator square root of 15 squared end root plus square root of 120 minus square root of 120 minus square root of 64 end fraction end cell row blank equals cell fraction numerator 4 square root of 15 plus 4 square root of 8 plus square root of 25 cross times 3 end root plus square root of 4 cross times 10 end root over denominator 15 minus 8 end fraction end cell row blank equals cell fraction numerator 4 square root of 15 plus 4 square root of 8 plus square root of 5 squared cross times 3 end root plus square root of 2 squared cross times 10 end root over denominator 7 end fraction end cell row blank equals cell fraction numerator 4 square root of 15 plus 4 square root of 8 plus 5 square root of 3 plus 2 square root of 10 over denominator 7 end fraction end cell end table

Jadi bentuk rasional dari fraction numerator 4 plus square root of 5 over denominator square root of 15 minus square root of 8 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 square root of 15 plus 4 square root of 8 plus 5 square root of 3 plus 2 square root of 10 over denominator 7 end fraction end cell end table.

h. Diketahui fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction maka cara merasionalkannya adalah dengan mengalikan penyebut dengan akar sekawannya yaitu 4 square root of 3 minus square root of 6 sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction end cell equals cell fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction cross times fraction numerator 4 square root of 3 minus square root of 6 over denominator 4 square root of 3 minus square root of 6 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 8 minus square root of 2 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses over denominator open parentheses 4 square root of 3 plus square root of 6 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 8 cross times 4 square root of 3 minus square root of 8 cross times square root of 6 minus square root of 2 cross times 4 square root of 3 plus square root of 2 cross times square root of 6 over denominator 4 square root of 3 cross times 4 square root of 3 minus 4 square root of 3 cross times square root of 6 plus square root of 6 cross times 4 square root of 3 minus square root of 6 cross times square root of 6 end fraction end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction end cell equals cell fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction cross times fraction numerator 4 square root of 3 minus square root of 6 over denominator 4 square root of 3 minus square root of 6 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 8 minus square root of 2 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses over denominator open parentheses 4 square root of 3 plus square root of 6 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 8 cross times 4 square root of 3 minus square root of 8 cross times square root of 6 minus square root of 2 cross times 4 square root of 3 plus square root of 2 cross times square root of 6 over denominator 4 square root of 3 cross times 4 square root of 3 minus 4 square root of 3 cross times square root of 6 plus square root of 6 cross times 4 square root of 3 minus square root of 6 cross times square root of 6 end fraction end cell row blank equals cell fraction numerator 4 square root of 8 cross times 3 end root minus square root of 8 cross times 6 end root minus 4 square root of 2 cross times 3 end root plus square root of 2 cross times 6 end root over denominator 16 square root of 3 cross times 3 end root minus 4 square root of 3 cross times 6 end root plus 4 square root of 6 cross times 3 end root minus square root of 6 cross times 6 end root end fraction end cell row blank equals cell fraction numerator 4 square root of 24 minus square root of 48 minus 4 square root of 6 plus square root of 12 over denominator 16 square root of 9 minus 4 square root of 18 plus 4 square root of 18 minus square root of 36 end fraction end cell end table

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction end cell equals cell fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction cross times fraction numerator 4 square root of 3 minus square root of 6 over denominator 4 square root of 3 minus square root of 6 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 8 minus square root of 2 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses over denominator open parentheses 4 square root of 3 plus square root of 6 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 8 cross times 4 square root of 3 minus square root of 8 cross times square root of 6 minus square root of 2 cross times 4 square root of 3 plus square root of 2 cross times square root of 6 over denominator 4 square root of 3 cross times 4 square root of 3 minus 4 square root of 3 cross times square root of 6 plus square root of 6 cross times 4 square root of 3 minus square root of 6 cross times square root of 6 end fraction end cell row blank equals cell fraction numerator 4 square root of 8 cross times 3 end root minus square root of 8 cross times 6 end root minus 4 square root of 2 cross times 3 end root plus square root of 2 cross times 6 end root over denominator 16 square root of 3 cross times 3 end root minus 4 square root of 3 cross times 6 end root plus 4 square root of 6 cross times 3 end root minus square root of 6 cross times 6 end root end fraction end cell row blank equals cell fraction numerator 4 square root of 24 minus square root of 48 minus 4 square root of 6 plus square root of 12 over denominator 16 square root of 9 minus 4 square root of 18 plus 4 square root of 18 minus square root of 36 end fraction end cell row blank equals cell fraction numerator 4 square root of 4 cross times 6 end root minus square root of 16 cross times 3 end root minus 4 square root of 6 plus square root of 4 cross times 3 end root over denominator 16 cross times 9 minus 6 end fraction end cell row blank equals cell fraction numerator 4 square root of 2 squared cross times 6 end root minus square root of 4 squared cross times 3 end root minus 4 square root of 6 plus square root of 2 squared cross times 3 end root over denominator 144 minus 6 end fraction end cell row blank equals cell fraction numerator 4 cross times 2 square root of 6 minus 4 square root of 3 minus 4 square root of 6 plus 2 square root of 3 over denominator 138 end fraction end cell row blank equals cell fraction numerator 8 square root of 6 minus 4 square root of 3 minus 4 square root of 6 plus 2 square root of 3 over denominator 138 end fraction end cell end table

Berdasarkan aturan penjumlahan dan pengurangan bentuk akar dengan bilangan pokok sama yaitu a n-th root of b plus-or-minus c n-th root of b equals open parentheses a plus-or-minus c close parentheses n-th root of b maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction end cell equals cell fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction cross times fraction numerator 4 square root of 3 minus square root of 6 over denominator 4 square root of 3 minus square root of 6 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 8 minus square root of 2 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses over denominator open parentheses 4 square root of 3 plus square root of 6 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 8 cross times 4 square root of 3 minus square root of 8 cross times square root of 6 minus square root of 2 cross times 4 square root of 3 plus square root of 2 cross times square root of 6 over denominator 4 square root of 3 cross times 4 square root of 3 minus 4 square root of 3 cross times square root of 6 plus square root of 6 cross times 4 square root of 3 minus square root of 6 cross times square root of 6 end fraction end cell row blank equals cell fraction numerator 4 square root of 8 cross times 3 end root minus square root of 8 cross times 6 end root minus 4 square root of 2 cross times 3 end root plus square root of 2 cross times 6 end root over denominator 16 square root of 3 cross times 3 end root minus 4 square root of 3 cross times 6 end root plus 4 square root of 6 cross times 3 end root minus square root of 6 cross times 6 end root end fraction end cell row blank equals cell fraction numerator 4 square root of 24 minus square root of 48 minus 4 square root of 6 plus square root of 12 over denominator 16 square root of 9 minus 4 square root of 18 plus 4 square root of 18 minus square root of 36 end fraction end cell row blank equals cell fraction numerator 4 square root of 4 cross times 6 end root minus square root of 16 cross times 3 end root minus 4 square root of 6 plus square root of 4 cross times 3 end root over denominator 16 cross times 9 minus 6 end fraction end cell row blank equals cell fraction numerator 4 square root of 2 squared cross times 6 end root minus square root of 4 squared cross times 3 end root minus 4 square root of 6 plus square root of 2 squared cross times 3 end root over denominator 144 minus 6 end fraction end cell row blank equals cell fraction numerator 4 cross times 2 square root of 6 minus 4 square root of 3 minus 4 square root of 6 plus 2 square root of 3 over denominator 138 end fraction end cell row blank equals cell fraction numerator 8 square root of 6 minus 4 square root of 3 minus 4 square root of 6 plus 2 square root of 3 over denominator 138 end fraction end cell row blank equals cell fraction numerator 8 square root of 6 minus 4 square root of 6 minus 4 square root of 3 plus 2 square root of 3 over denominator 138 end fraction end cell row blank equals cell fraction numerator open parentheses 8 minus 4 close parentheses square root of 6 minus open parentheses 4 minus 2 close parentheses square root of 3 over denominator 138 end fraction end cell row blank equals cell fraction numerator 4 square root of 6 minus 2 square root of 3 over denominator 138 end fraction end cell end table

Jadi bentuk rasional dari fraction numerator square root of 8 minus square root of 2 over denominator 4 square root of 3 plus square root of 6 end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 square root of 6 minus 2 square root of 3 over denominator 138 end fraction end cell end table.

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