Rasionalkan penyebut bentuk-bentuk akar berikut. d. 7−323+3

Pertanyaan

Rasionalkan penyebut bentuk-bentuk akar berikut.

d. $fraction numerator 2 square root of 3 plus 3 over denominator square root of 7 minus square root of 3 end fraction$

Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

rasinal dari $fraction numerator 2 square root of 3 plus 3 over denominator square root of 7 minus square root of 3 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 21 plus 3 open parentheses square root of 7 plus square root of 3 close parentheses plus 6 over denominator 4 end fraction end cell end table$ .

Pembahasan

Bentuk $fraction numerator 2 square root of 3 plus 3 over denominator square root of 7 minus square root of 3 end fraction$ dapat dirasionalkan penyebutnya menjadi

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 square root of 3 plus 3 over denominator square root of 7 minus square root of 3 end fraction times fraction numerator square root of 7 plus square root of 3 over denominator square root of 7 plus square root of 3 end fraction end cell equals cell fraction numerator 2 square root of 3 times square root of 7 plus 2 square root of 3 times square root of 3 plus 3 square root of 7 plus 3 square root of 3 over denominator square root of 7 times square root of 7 minus square root of 7 times square root of 3 plus square root of 7 times square root of 3 minus square root of 3 times square root of 3 end fraction end cell row blank equals cell fraction numerator 2 square root of 21 plus 2 square root of 9 plus 3 square root of 7 plus 3 square root of 3 over denominator open parentheses square root of 49 minus square root of 9 close parentheses end fraction end cell row blank equals cell fraction numerator 2 square root of 21 plus 2 times 3 plus 3 square root of 7 plus 3 square root of 3 over denominator open parentheses 7 minus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 2 square root of 21 plus 3 open parentheses square root of 7 plus square root of 3 close parentheses plus 6 over denominator 4 end fraction end cell end table end style$

Jadi, rasinal dari $fraction numerator 2 square root of 3 plus 3 over denominator square root of 7 minus square root of 3 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 21 plus 3 open parentheses square root of 7 plus square root of 3 close parentheses plus 6 over denominator 4 end fraction end cell end table$ .