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Bentuk sederhana dari  adalah ...

Pertanyaan

Bentuk sederhana dari fraction numerator square root of 6 over denominator 3 square root of 2 plus 2 square root of 3 end fraction adalah ...

  1. square root of 3 minus 2 over 3 square root of 3 

  2. square root of 3 minus square root of 2 

  3. square root of 2 plus 2 over 3 square root of 3 

  4. square root of 3 plus 2 over 3 square root of 2 

  5. square root of 2 minus square root of 3 

Pembahasan Soal:

Dengan mengalikan dengan akar sekawan dari penyebut diperoleh 

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

Dengan demikian, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Rante

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 04 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Kerjakan soal berikut ini. Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Untuk menyederhanakan suatu pecahan dalam bentuk akar, dapat dilakukan operasi aljabar berupa kali sekawan sebagai berikut

3+23====3+23×3232343(32)13(32)3(32)

Jadi, jawaban yang tepat adalah E.

Roboguru

Tentukan bentuk sederhana dari  !

Pembahasan Soal:

Untuk mencari bentuk sederhana dari soal tersebut adalah dengan merasionalkan penyebut pecahan tersebut. Pecahan bentuk fraction numerator a over denominator b plus square root of c end fraction diselesaikan dengan mengalikan fraction numerator b minus square root of c over denominator b minus square root of c end fraction. Sehingga cara ini juga dapat kita gunakan untuk soal tersebut, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 plus 4 square root of 2 over denominator 3 plus square root of 2 end fraction end cell equals cell fraction numerator 2 plus 4 square root of 2 over denominator 3 plus square root of 2 end fraction cross times fraction numerator 3 minus square root of 2 over denominator 3 minus square root of 2 end fraction end cell row blank equals cell fraction numerator open parentheses 2 plus 4 square root of 2 close parentheses open parentheses 3 minus square root of 2 close parentheses over denominator open parentheses 3 plus square root of 2 close parentheses open parentheses 3 minus square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator 6 plus 12 square root of 2 minus 2 square root of 2 minus 8 over denominator 9 minus 2 end fraction end cell row blank equals cell fraction numerator 10 square root of 2 minus 2 over denominator 7 end fraction end cell row blank equals cell fraction numerator 2 open parentheses 5 square root of 2 minus 1 close parentheses over denominator 7 end fraction end cell row blank equals cell 2 over 7 open parentheses 5 square root of 2 minus 1 close parentheses end cell end table 

Dengan demikian, bentuk sederhana dari fraction numerator 2 plus 4 square root of 2 over denominator 3 plus square root of 2 end fraction adalah 2 over 7 open parentheses 5 square root of 2 minus 1 close parentheses.

Roboguru

Bentuk rasional dari  adalah....

Pembahasan Soal:

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 over denominator 3 plus square root of 2 end fraction blank end cell equals cell fraction numerator 2 over denominator 3 plus square root of 2 end fraction cross times blank fraction numerator 3 minus square root of 2 over denominator 3 minus square root of 2 end fraction end cell row blank equals cell blank fraction numerator 2 blank left parenthesis 3 minus square root of 2 right parenthesis over denominator 3 squared minus left parenthesis square root of 2 right parenthesis squared end fraction end cell row blank equals cell blank fraction numerator 2 blank left parenthesis 3 minus square root of 2 right parenthesis over denominator 9 minus 2 end fraction end cell row blank equals cell blank fraction numerator 6 minus 2 square root of 2 over denominator 7 end fraction end cell end table end style  

Jadi, bentuk rasional dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator size 14px 2 over denominator size 14px 3 size 14px plus square root of size 14px 2 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank blank end table adalah begin mathsize 14px style end stylebegin mathsize 14px style fraction numerator 6 minus 2 square root of 2 over denominator 7 end fraction end style.

Dengan demikian, jawaban yang tepat adalah B.space  

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Ingat

begin mathsize 14px style open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared end style 

Maka

begin mathsize 12px style fraction numerator square root of 18 minus 8 square root of 5 end root over denominator 3 minus square root of 3 end fraction plus fraction numerator square root of 6 over denominator 2 square root of 3 plus square root of 6 end fraction equals open parentheses fraction numerator square root of 18 minus 2 times 4 square root of 5 end root over denominator 3 minus square root of 3 end fraction cross times fraction numerator 3 plus square root of 3 over denominator 3 plus square root of 3 end fraction close parentheses plus open parentheses fraction numerator square root of 6 over denominator 2 square root of 3 plus square root of 6 end fraction cross times fraction numerator 2 square root of 3 minus square root of 6 over denominator 2 square root of 3 minus square root of 6 end fraction close parentheses equals open parentheses fraction numerator open parentheses square root of 18 minus 2 square root of 80 end root close parentheses open parentheses 3 plus square root of 3 close parentheses over denominator 3 squared minus open parentheses square root of 3 close parentheses squared end fraction close parentheses plus open parentheses fraction numerator square root of 6 open parentheses 2 square root of 3 minus square root of 6 close parentheses over denominator open parentheses 2 square root of 3 close parentheses squared minus open parentheses square root of 6 close parentheses squared end fraction close parentheses equals open parentheses fraction numerator open parentheses square root of left parenthesis 10 plus 8 right parenthesis minus 2 square root of 10 times 8 end root end root close parentheses open parentheses 3 plus square root of 3 close parentheses over denominator 9 minus 3 end fraction close parentheses plus open parentheses fraction numerator open parentheses square root of 6 times 2 square root of 3 close parentheses minus open parentheses square root of 6 times square root of 6 close parentheses over denominator 12 minus 6 end fraction close parentheses equals open parentheses fraction numerator open parentheses square root of 10 minus square root of 8 close parentheses open parentheses 3 plus square root of 3 close parentheses over denominator 6 end fraction close parentheses plus open parentheses fraction numerator 2 square root of 18 minus 6 over denominator 6 end fraction close parentheses equals fraction numerator open parentheses square root of 10 times 3 close parentheses minus open parentheses square root of 8 times 3 close parentheses plus open parentheses square root of 10 times square root of 3 close parentheses minus open parentheses square root of 8 times square root of 3 close parentheses plus open parentheses 2 square root of 9 times 2 end root minus 6 close parentheses over denominator 6 end fraction equals fraction numerator 3 square root of 10 minus 3 square root of 8 plus square root of 30 minus square root of 24 plus 6 square root of 2 minus 6 over denominator 6 end fraction equals fraction numerator 3 square root of 10 minus 3 times 2 square root of 2 plus square root of 30 minus 2 square root of 6 plus 6 square root of 2 minus 6 over denominator 6 end fraction equals fraction numerator 3 square root of 10 minus 6 square root of 2 plus square root of 30 minus 2 square root of 6 plus 6 square root of 2 minus 6 over denominator 6 end fraction equals fraction numerator square root of 30 plus 3 square root of 10 minus 2 square root of 6 minus 6 square root of 2 plus 6 square root of 2 minus 6 over denominator 6 end fraction equals fraction numerator square root of 30 plus 3 square root of 10 minus 2 square root of 6 minus 6 over denominator 6 end fraction end style 

Jadi, hasil dari undefined adalah undefined.

Dengan demikian, jawaban yang tepat adalah A.

 

Roboguru

Bentuk rasional dari adalah ....

Pembahasan Soal:

Perhatikan bahwa

begin mathsize 12px style fraction numerator square root of 6 minus square root of 3 over denominator 5 plus square root of 15 end fraction equals blank fraction numerator square root of 6 minus square root of 3 over denominator 5 plus square root of 15 end fraction cross times fraction numerator 5 minus square root of 15 over denominator 5 minus square root of 15 end fraction equals fraction numerator open parentheses square root of 6 cross times 5 close parentheses minus open parentheses square root of 3 cross times 5 close parentheses minus open parentheses square root of 6 cross times square root of 15 close parentheses plus left parenthesis square root of 3 cross times square root of 15 right parenthesis over denominator 5 squared minus open parentheses square root of 15 close parentheses squared end fraction equals fraction numerator 5 square root of 6 minus 5 square root of 3 minus square root of 90 plus square root of 45 over denominator 25 minus 15 end fraction equals fraction numerator 5 square root of 6 minus 5 square root of 3 minus square root of 9 cross times 10 end root plus square root of 9 cross times 5 end root over denominator 10 end fraction equals fraction numerator 5 square root of 6 minus 5 square root of 3 minus 3 square root of 10 plus 3 square root of 5 over denominator 10 end fraction equals fraction numerator 3 square root of 5 plus 5 square root of 6 minus 5 square root of 3 minus 3 square root of 10 over denominator 10 end fraction end style   

Jadi, bentuk rasional dari begin mathsize 14px style fraction numerator square root of 6 minus square root of 3 over denominator 5 plus square root of 15 end fraction end style adalah undefined.

Dengan demikian, jawaban yang tepat adalah D.

Roboguru

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