Pertanyaan

Bentuk sederhana dari 2 2 − 5 9 = ...

Bentuk sederhana dari $\frac{9}{2 2 - 5}$ = ...

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

$begin mathsize 12px style fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction equals 6 square root of 2 plus 3 square root of 5 end style$

Pembahasan

Penyederhanaan bentuk akar dapat dilakukan dengan mengalikan bentuk akar tersebut dengan akar sekawan Jadi,

Penyederhanaan bentuk akar dapat dilakukan dengan mengalikan bentuk akar tersebut dengan akar sekawan

$begin mathsize 12px style fraction numerator a over denominator b square root of b minus square root of c end fraction equals fraction numerator a over denominator b square root of b minus square root of c end fraction cross times fraction numerator open parentheses b square root of b plus square root of c close parentheses over denominator open parentheses b square root of b plus square root of c close parentheses end fraction equals fraction numerator a open parentheses b square root of b plus square root of c close parentheses over denominator b cubed minus c end fraction fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction equals fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction cross times fraction numerator open parentheses 2 square root of 2 plus square root of 5 close parentheses over denominator open parentheses 2 square root of 2 plus square root of 5 close parentheses end fraction equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 4 cross times 2 minus 5 end fraction equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 8 minus 5 end fraction equals fraction numerator 18 square root of 2 plus 9 square root of 5 over denominator 3 end fraction equals 6 square root of 2 plus 3 square root of 5 end style$

Jadi, $begin mathsize 12px style fraction numerator 9 over denominator 2 square root of 2 minus square root of 5 end fraction equals 6 square root of 2 plus 3 square root of 5 end style$