Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut! 5 − 2 5 + 2

Rasionalkan penyebut pecahan-pecahan berikut!

$\frac{5 + 2}{5 - 2}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

bentuk rasional dari adalah .

bentuk rasional dari $fraction numerator square root of 5 plus 2 over denominator square root of 5 minus square root of 2 end fraction$ adalah 1 third left parenthesis 5 plus square root of 10 plus 2 square root of 5 plus 2 square root of 2 right parenthesis

1 third left parenthesis 5 plus square root of 10 plus 2 square root of 5 plus 2 square root of 2 right parenthesis

Pembahasan

Ingat kembali cara merasionalkan bentuk akar berikut! Dengan rumus di atas, diperoleh perhitungan sebagai berikut. Jadi, bentuk rasional dari adalah .

Ingat kembali cara merasionalkan bentuk akar berikut!

$fraction numerator 1 over denominator square root of a plus square root of b end fraction equals fraction numerator 1 over denominator square root of a plus square root of b end fraction cross times fraction numerator square root of a minus square root of b over denominator square root of a minus square root of b end fraction$

Dengan rumus di atas, diperoleh perhitungan sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 5 plus 2 over denominator square root of 5 minus square root of 2 end fraction end cell equals cell fraction numerator square root of 5 plus 2 over denominator square root of 5 minus square root of 2 end fraction cross times fraction numerator square root of 5 plus square root of 2 over denominator square root of 5 plus square root of 2 end fraction end cell row blank equals cell fraction numerator left parenthesis square root of 5 plus 2 right parenthesis left parenthesis square root of 5 plus square root of 2 right parenthesis over denominator left parenthesis square root of 5 minus square root of 2 right parenthesis left parenthesis square root of 5 plus square root of 2 right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis square root of 5 right parenthesis left parenthesis square root of 5 right parenthesis plus left parenthesis square root of 5 right parenthesis left parenthesis square root of 2 right parenthesis plus 2 left parenthesis square root of 5 right parenthesis end root plus 2 left parenthesis square root of 2 right parenthesis over denominator left parenthesis square root of 5 right parenthesis squared minus left parenthesis square root of 2 right parenthesis squared end fraction end cell row blank equals cell fraction numerator 5 plus square root of 5 cross times 2 end root plus 2 square root of 5 plus 2 square root of 2 over denominator 5 minus 2 end fraction end cell row blank equals cell fraction numerator 5 plus square root of 10 plus 2 square root of 5 plus 2 square root of 2 over denominator 3 end fraction end cell row blank equals cell 1 third left parenthesis 5 plus square root of 10 plus 2 square root of 5 plus 2 square root of 2 right parenthesis end cell end table$

Jadi, bentuk rasional dari $fraction numerator square root of 5 plus 2 over denominator square root of 5 minus square root of 2 end fraction$ adalah 1 third left parenthesis 5 plus square root of 10 plus 2 square root of 5 plus 2 square root of 2 right parenthesis .