Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut! 11 − 7 7

Rasionalkan penyebut pecahan-pecahan berikut!

$\frac{7}{11 - 7}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan dapat dirasionalkan penyebutnya menjadi .

pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 7 over denominator square root of 11 minus square root of 7 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 77 plus 7 over denominator 4 end fraction end cell end table$ .

Pembahasan

Ingat kembali aturan berikut. Sehingga dapat dirasionalkan penyebut pecahan sebagai berikut. Dengan demikian, pecahan dapat dirasionalkan penyebutnya menjadi .

Ingat kembali aturan berikut.

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

Sehingga dapat dirasionalkan penyebut pecahan $fraction numerator square root of 7 over denominator square root of 11 minus square root of 7 end fraction$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 7 over denominator square root of 11 minus square root of 7 end fraction end cell equals cell fraction numerator square root of 7 over denominator square root of 11 minus square root of 7 end fraction cross times fraction numerator square root of 11 plus square root of 7 over denominator square root of 11 plus square root of 7 end fraction end cell row blank equals cell fraction numerator square root of 7 open parentheses square root of 11 plus square root of 7 close parentheses over denominator open parentheses square root of 11 minus square root of 7 close parentheses open parentheses square root of 11 plus square root of 7 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 7 cross times 11 end root plus 7 over denominator 11 minus 7 end fraction end cell row blank equals cell fraction numerator square root of 77 plus 7 over denominator 4 end fraction end cell end table$

Dengan demikian, pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 7 over denominator square root of 11 minus square root of 7 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 77 plus 7 over denominator 4 end fraction end cell end table$ .