Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut! 12 − 6 3 + 4

Rasionalkan penyebut pecahan-pecahan berikut!

$\frac{3 + 4}{12 - 6}$

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Habis dalam

Klaim

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan dapat dirasionalkan penyebutnya menjadi .

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

table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 4 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 6 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 $fraction numerator 1 over denominator square root of a minus square root of b end fraction$ dapat dilakukan dengan rumus dan prosedur sebagai 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 $fraction numerator square root of 3 plus 4 over denominator square root of 12 minus square root of 6 end fraction$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 3 plus 4 over denominator square root of 12 minus square root of 6 end fraction end cell equals cell fraction numerator square root of 3 plus 4 over denominator square root of 12 minus square root of 6 end fraction cross times fraction numerator square root of 12 plus square root of 6 over denominator square root of 12 plus square root of 6 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 3 plus 4 close parentheses open parentheses square root of 12 plus square root of 6 close parentheses over denominator open parentheses square root of 12 minus square root of 6 close parentheses open parentheses square root of 12 plus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 3 cross times 12 end root plus 4 square root of 12 plus square root of 3 cross times 6 end root plus 4 square root of 6 over denominator open parentheses square root of 12 close parentheses squared minus open parentheses square root of 6 close parentheses squared end fraction end cell row blank equals cell fraction numerator square root of 36 plus 4 square root of 12 plus square root of 18 plus 4 square root of 6 over denominator 12 minus 6 end fraction end cell row blank equals cell fraction numerator 6 plus open parentheses 4 cross times 2 square root of 3 close parentheses plus 3 square root of 2 plus 4 square root of 6 over denominator 6 end fraction end cell row blank equals cell fraction numerator 6 plus 8 square root of 3 plus 3 square root of 2 plus 4 square root of 6 over denominator 6 end fraction end cell row blank equals cell 1 plus 4 over 3 square root of 3 plus 1 half square root of 2 plus 2 over 3 square root of 6 end cell end table$

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