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Rasionalkan bentuk akar

Pertanyaan

Rasionalkan bentuk akar fraction numerator 3 over denominator square root of 5 end fraction 

Pembahasan Soal:

Untuk merasionalkan bentuk akar, maka kita perlu kalikan dengan akar sekawannya. Perhatikan penghitungan berikut!

 fraction numerator 3 over denominator square root of 5 end fraction equals fraction numerator 3 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction fraction numerator 3 over denominator square root of 5 end fraction equals fraction numerator 3 square root of 5 over denominator square root of 25 end fraction fraction numerator 3 over denominator square root of 5 end fraction equals fraction numerator 3 square root of 5 over denominator 5 end fraction   

Jadi, bentuk sederhananya adalah fraction numerator 3 square root of 5 over denominator 5 end fraction. 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Fatimatuzzahroh

Mahasiswa/Alumni Institut Pertanian Bogor

Terakhir diupdate 04 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Bentuk sederhana dari  adalah

Pembahasan Soal:

  • Menyederhanakan bentuk akar dengan mengalikan dengan akar sekawan:

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

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Pembahasan Soal:

Diasumsikan soal tersebut adalah mencari bentuk rasional.

Untuk mencari bentuk rasional dari pecahan bentuk fraction numerator straight a over denominator straight b plus square root of straight c end fraction adalah dengan mengalikannya dengan fraction numerator straight b minus square root of straight c over denominator straight b minus square root of straight c end fraction 

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 over denominator 1 plus square root of 3 end fraction end cell equals cell fraction numerator 2 over denominator 1 plus square root of 3 end fraction cross times fraction numerator 1 minus square root of 3 over denominator 1 minus square root of 3 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 1 minus square root of 3 right parenthesis over denominator left parenthesis 1 plus square root of 3 right parenthesis left parenthesis 1 minus square root of 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 1 minus square root of 3 right parenthesis over denominator 1 plus square root of 3 minus square root of 3 minus 3 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 1 minus square root of 3 right parenthesis over denominator 1 minus 3 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 1 minus square root of 3 right parenthesis over denominator negative 2 end fraction end cell row blank equals cell negative 1 left parenthesis 1 minus square root of 3 right parenthesis end cell row blank equals cell negative 1 plus square root of 3 end cell row blank equals cell square root of 3 minus 1 end cell end table   

Jadi, nilai dari fraction numerator 2 over denominator 1 plus square root of 3 end fraction adalah square root of 3 minus 1   

1

Roboguru

Rasionalkan penyebut dari bilangan-bilangan berikut! c.

Pembahasan Soal:

Rasionalkan dengan cara perkalian sekawan sebagai berikut.

\begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 7 minus square root of 5 over denominator square root of 5 minus square root of 8 end fraction end cell equals cell fraction numerator square root of 7 minus square root of 5 over denominator square root of 5 minus square root of 8 end fraction cross times fraction numerator square root of 5 plus square root of 8 over denominator square root of 5 plus square root of 8 end fraction end cell row blank equals cell fraction numerator square root of 35 plus square root of 56 minus 5 minus square root of 40 over denominator 5 minus 8 end fraction end cell row blank equals cell fraction numerator square root of 35 plus 2 square root of 14 minus 5 minus 2 square root of 10 over denominator negative 3 end fraction end cell row blank equals cell negative 1 third open parentheses square root of 35 minus 5 close parentheses minus 2 over 3 open parentheses square root of 14 minus square root of 10 close parentheses end cell end table end style

Jadi, bentuk rasional dari begin mathsize 12px style fraction numerator square root of 7 minus square root of 5 over denominator square root of 5 minus square root of 8 end fraction end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses square root of 35 minus 5 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses square root of 14 minus square root of 10 close parentheses end cell end table end style.

0

Roboguru

Bentuk dirasionalkan penyebutnya adalah....

Pembahasan Soal:

fraction numerator 3 over denominator square root of 5 end fraction space. fraction numerator square root of 5 over denominator square root of 5 end fraction equals fraction numerator 3 square root of 5 over denominator 5 end fraction equals 3 over 5 square root of 5

0

Roboguru

Rasionalkan setiap bentuk akar berikut. d).

Pembahasan Soal:

Ingat:

begin mathsize 14px style fraction numerator 1 over denominator square root of a minus square root of b end fraction equals fraction numerator 1 over denominator square root of a minus square root of b end fraction cross times fraction numerator square root of a plus square root of b over denominator square root of a plus square root of b end fraction equals fraction numerator square root of a plus square root of b over denominator a minus b end fraction end style

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 over denominator square root of 5 minus square root of 3 end fraction end cell equals cell fraction numerator 6 over denominator square root of 5 minus square root of 3 end fraction cross times fraction numerator square root of 5 plus square root of 3 over denominator square root of 5 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator open parentheses square root of 5 minus square root of 3 close parentheses open parentheses square root of 5 plus square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator 5 minus 3 end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator 2 end fraction end cell row blank equals cell 3 open parentheses square root of 5 plus square root of 3 close parentheses end cell end table end style

Jadi, jawaban yang tepat adalah begin mathsize 14px style 3 open parentheses square root of 5 plus square root of 3 close parentheses end style.

3

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Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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