Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut! 4 3 + 6 8 + 7

Rasionalkan penyebut pecahan-pecahan berikut!

$\frac{8 + 7}{4 3 + 6}$

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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 $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 8 plus square root of 7 over denominator 4 square root of 3 plus square root of 6 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 square root of 6 over denominator 21 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 21 over denominator 21 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 3 over denominator 21 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 42 over denominator 42 end fraction end cell end table$ .

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 $fraction numerator 1 over denominator square root of a plus square root of b end fraction$ dapat dilakukan dengan rumus dan prosedur sebagai berikut.

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

Sehingga dapat dirasionalkan penyebut pecahan $fraction numerator square root of 8 plus square root of 7 over denominator 4 square root of 3 plus square root of 6 end fraction$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 8 plus square root of 7 over denominator 4 square root of 3 plus square root of 6 end fraction end cell equals cell fraction numerator square root of 8 plus square root of 7 over denominator 4 square root of 3 plus square root of 6 end fraction cross times fraction numerator 4 square root of 3 minus square root of 6 over denominator 4 square root of 3 minus square root of 6 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 8 plus square root of 7 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses over denominator open parentheses 4 square root of 3 plus square root of 6 close parentheses open parentheses 4 square root of 3 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator 4 square root of 8 cross times 3 end root plus 4 square root of 7 cross times 3 end root minus square root of 8 cross times 6 end root minus square root of 7 cross times 6 end root over denominator open parentheses 4 square root of 3 close parentheses squared minus open parentheses square root of 6 close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 4 square root of 24 close parentheses plus 4 square root of 21 minus square root of 48 minus square root of 42 over denominator open parentheses 16 cross times 3 close parentheses minus 6 end fraction end cell row blank equals cell fraction numerator 8 square root of 6 plus 4 square root of 21 minus 4 square root of 3 minus square root of 42 over denominator 48 minus 6 end fraction end cell row blank equals cell fraction numerator 8 square root of 6 plus 4 square root of 21 minus 4 square root of 3 minus square root of 42 over denominator 42 end fraction end cell row blank equals cell fraction numerator 4 square root of 6 over denominator 21 end fraction plus fraction numerator 2 square root of 21 over denominator 21 end fraction minus fraction numerator 2 square root of 3 over denominator 21 end fraction minus fraction numerator square root of 42 over denominator 42 end fraction end cell end table$

Dengan demikian, pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 8 plus square root of 7 over denominator 4 square root of 3 plus square root of 6 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 square root of 6 over denominator 21 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 21 over denominator 21 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 3 over denominator 21 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 42 over denominator 42 end fraction end cell end table$ .