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Rasionalkan penyebut pecahan-pecahan berikut! 23​−2​15​+25​​

Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut!

fraction numerator square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction end cell end table dapat dirasionalkan penyebutnya menjadi 3 over 5 square root of 5 plus square root of 3 plus 1 over 10 square root of 30 plus 1 half square root of 2.

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 square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction end cell equals cell fraction numerator square root of 15 plus 5 over denominator 2 square root of 3 minus square root of 2 end fraction cross times fraction numerator 2 square root of 3 plus square root of 2 over denominator 2 square root of 3 plus square root of 2 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 15 plus 5 close parentheses open parentheses 2 square root of 3 plus square root of 2 close parentheses over denominator open parentheses 2 square root of 3 minus square root of 2 close parentheses open parentheses 2 square root of 3 plus square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator 2 square root of 15 cross times 3 end root plus 10 square root of 3 plus square root of 15 cross times 2 end root plus 5 square root of 2 over denominator open parentheses 2 square root of 3 close parentheses squared minus open parentheses square root of 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 square root of 45 plus 10 square root of 3 plus square root of 30 plus 5 square root of 2 over denominator 12 minus 2 end fraction end cell row blank equals cell fraction numerator open parentheses 2 cross times 3 square root of 5 close parentheses plus 10 square root of 3 plus square root of 30 plus 5 square root of 2 over denominator 10 end fraction end cell row blank equals cell fraction numerator 6 square root of 5 plus 10 square root of 3 plus square root of 30 plus 5 square root of 2 over denominator 10 end fraction end cell row blank equals cell 3 over 5 square root of 5 plus square root of 3 plus 1 over 10 square root of 30 plus 1 half square root of 2 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 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction end cell end table dapat dirasionalkan penyebutnya menjadi 3 over 5 square root of 5 plus square root of 3 plus 1 over 10 square root of 30 plus 1 half square root of 2.

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