Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut! 4 12 8 − 6

Rasionalkan penyebut pecahan-pecahan berikut!

$\frac{8 - 6}{4 12}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan dapat dirasionalkan penyebutnya menjadi .

pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 8 minus 6 over denominator 4 square root of 12 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 6 minus 3 square root of 3 over denominator 12 end fraction end cell end table$ .

Pembahasan

Untuk merasionalkan penyebut pecahan berbentuk dapat dilakukan dengan rumus dan prosedur sebagai berikut. Sehingga dapat dirasionalkan penyebut pecahan sebagai berikut. Dengan demikian, pecahan dapat dirasionalkan penyebutnya menjadi .

Untuk merasionalkan penyebut pecahan berbentuk $fraction numerator a over denominator square root of b end fraction comma space fraction numerator 1 over denominator a plus square root of b end fraction comma space fraction numerator 1 over denominator a minus square root of b end fraction$ dapat dilakukan dengan rumus dan prosedur sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator square root of b end fraction end cell equals cell fraction numerator a over denominator square root of b end fraction cross times fraction numerator square root of b over denominator square root of b end fraction end cell row cell fraction numerator 1 over denominator a plus square root of b end fraction end cell equals cell fraction numerator 1 over denominator a plus square root of b end fraction cross times fraction numerator a minus square root of b over denominator a minus square root of b end fraction end cell row cell fraction numerator 1 over denominator a minus square root of b end fraction end cell equals cell fraction numerator 1 over denominator a minus square root of b end fraction cross times fraction numerator a plus square root of b over denominator a plus square root of b end fraction end cell end table$

Sehingga dapat dirasionalkan penyebut pecahan $fraction numerator square root of 8 minus 6 over denominator 4 square root of 12 end fraction$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 8 minus 6 over denominator 4 square root of 12 end fraction end cell equals cell fraction numerator square root of 8 minus 6 over denominator 4 square root of 12 end fraction cross times fraction numerator square root of 12 over denominator square root of 12 end fraction end cell row blank equals cell fraction numerator square root of 8 cross times 12 end root minus 6 square root of 12 over denominator 4 square root of 12 cross times 12 end root end fraction end cell row blank equals cell fraction numerator square root of 96 minus 6 square root of 12 over denominator 4 cross times 12 end fraction end cell row blank equals cell fraction numerator square root of 16 cross times 6 end root minus 6 square root of 4 cross times 3 end root over denominator 48 end fraction end cell row blank equals cell fraction numerator 4 square root of 6 minus 12 square root of 3 over denominator 48 end fraction end cell row blank equals cell fraction numerator square root of 6 minus 3 square root of 3 over denominator 12 end fraction end cell end table$

Dengan demikian, pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 8 minus 6 over denominator 4 square root of 12 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 6 minus 3 square root of 3 over denominator 12 end fraction end cell end table$ .