Roboguru

Hasil dari  adalah

Pertanyaan

Hasil dari square root of 48 adalah horizontal ellipsis 

  1. 3 square root of 2 

  2. 4 square root of 3 

  3. 6 square root of 3 

  4. 77 square root of 2 

Pembahasan Soal:

Perhatikan penyederhanaan bentuk akar berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 48 end cell equals cell square root of 16 times 3 end root end cell row blank equals cell square root of 16 times square root of 3 end cell row blank equals cell 4 square root of 3 end cell end table

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Sri

Mahasiswa/Alumni Universitas Muhammadiyah Purworejo

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Bentuk rasional dari  adalah

Pembahasan Soal:

Merasionalkan penyebut bentuk akar dapat dilakukan dengan mengalikan penyebutnya dengan akar sekawannya sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator square root of b end fraction end cell equals cell fraction numerator 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 end cell row blank equals cell fraction numerator a square root of b over denominator b end fraction end cell end table

Sehingga fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction end cell equals cell fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 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 3 square root of 6 plus square root of 5 close parentheses square root of 8 over denominator 4 cross times 8 end fraction end cell row blank equals cell fraction numerator 3 square root of 6 cross times square root of 8 plus square root of 5 cross times square root of 8 over denominator 32 end fraction end cell end table

Berdasarkan aturan perkalian bentuk akar dengan bilangan 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 comma space a not equal to 0 space text dan end text space b not equal to 0

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction end cell equals cell fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 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 3 square root of 6 plus square root of 5 close parentheses square root of 8 over denominator 4 cross times 8 end fraction end cell row blank equals cell fraction numerator 3 square root of 6 cross times square root of 8 plus square root of 5 cross times square root of 8 over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 square root of 6 cross times 8 end root plus square root of 5 cross times 8 end root over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 square root of 48 plus square root of 40 over denominator 32 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 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction end cell equals cell fraction numerator 3 square root of 48 plus square root of 40 over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 square root of 16 cross times 3 end root plus square root of 4 cross times 10 end root over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 square root of 4 squared cross times 3 end root plus square root of 2 squared cross times 10 end root over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 cross times 4 square root of 3 plus 2 square root of 10 over denominator 32 end fraction end cell row blank equals cell fraction numerator 12 square root of 3 plus 2 square root of 10 over denominator 32 end fraction end cell row blank equals cell fraction numerator up diagonal strike 2 open parentheses 6 square root of 3 plus square root of 10 close parentheses over denominator begin display style stack up diagonal strike 32 with 16 below end style end fraction end cell row blank equals cell fraction numerator 6 square root of 3 plus square root of 10 over denominator 16 end fraction end cell end table

Jadi bentuk rasional dari fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction adalah fraction numerator 6 square root of 3 plus square root of 10 over denominator 16 end fraction.

Oleh karena itu, jawaban yang benar adalah A.

1

Roboguru

Hasil dari adalah ....

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.

0

Roboguru

Rasionalkan penyebut pecahan-pecachan berikut!

Pembahasan Soal:

Ingat kembali aturan berikut.

  • square root of a squared cross times b end root equals a square root of b 
  • 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 

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 5 over denominator square root of 24 end fraction end cell equals cell fraction numerator square root of 5 over denominator square root of 2 squared cross times 6 end root end fraction end cell row blank equals cell fraction numerator square root of 5 over denominator 2 square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 5 over denominator 2 square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 5 cross times 6 end root over denominator 2 cross times 6 end fraction end cell row blank equals cell fraction numerator square root of 30 over denominator 12 end fraction end cell row blank equals cell 1 over 12 square root of 30 end cell end table 

Jadi, hasil dari merasionalkan fraction numerator square root of 5 over denominator square root of 24 end fraction adalah 1 over 12 square root of 30.

0

Roboguru

Bentuk sederhana dari adalah ...

Pembahasan Soal:

Ingat cara mnyederhanakan suatu bentuk pecahan dengan penyebut terdapat suatu akar dengan mengkalikan dengan sekawannya, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 over denominator 4 minus square root of 13 end fraction end cell equals cell fraction numerator 6 over denominator 4 minus square root of 13 end fraction cross times fraction numerator 4 plus square root of 13 over denominator 4 plus square root of 13 end fraction end cell row blank equals cell fraction numerator 6 left parenthesis 4 plus square root of 13 right parenthesis over denominator 4 squared minus open parentheses square root of 13 close parentheses squared end fraction end cell row blank equals cell fraction numerator 24 plus 6 square root of 13 over denominator 16 minus 13 end fraction end cell row blank equals cell fraction numerator 24 plus 6 square root of 13 over denominator 3 end fraction end cell row blank equals cell 8 plus 2 square root of 13 end cell row blank blank blank end table

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Rasionalkan penyebut pecahan-pecahan berikut! e.  f.  g.  h.

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.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved