Rasionalkan penyebut pecahan-pecahan berikut! 8​−3​102​​

Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut!

fraction numerator 10 square root of 2 over denominator square root of 8 minus square root of 3 end fraction

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan fraction numerator 10 square root of 2 over denominator square root of 8 minus square root of 3 end fraction dapat dirasionalkan penyebutnya menjadi 8 plus 2 square root of 6.

Pembahasan

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 10 square root of 2 over denominator square root of 8 minus square root of 3 end fraction sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 10 square root of 2 over denominator square root of 8 minus square root of 3 end fraction end cell equals cell fraction numerator 10 square root of 2 over denominator square root of 8 minus square root of 3 end fraction cross times fraction numerator square root of 8 plus square root of 3 over denominator square root of 8 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 10 square root of 2 open parentheses square root of 8 plus square root of 3 close parentheses over denominator open parentheses square root of 8 minus square root of 3 close parentheses open parentheses square root of 8 plus square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator 10 square root of 2 cross times 8 end root plus 10 square root of 2 cross times 3 end root over denominator open parentheses square root of 8 close parentheses squared minus open parentheses square root of 3 close parentheses squared end fraction end cell row blank equals cell fraction numerator 10 square root of 16 plus 10 square root of 6 over denominator 8 minus 3 end fraction end cell row blank equals cell fraction numerator open parentheses 10 cross times 4 close parentheses plus 10 square root of 6 over denominator 5 end fraction end cell row blank equals cell fraction numerator 40 plus 10 square root of 6 over denominator 5 end fraction end cell row blank equals cell 8 plus 2 square root of 6 end cell end table  

Dengan demikian, pecahan fraction numerator 10 square root of 2 over denominator square root of 8 minus square root of 3 end fraction dapat dirasionalkan penyebutnya menjadi 8 plus 2 square root of 6.

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