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Rasionalkan penyebut pecahan-pecahan berikut! 18​−5​18​+5​​

Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut!

fraction numerator square root of 18 plus square root of 5 over denominator square root of 18 minus square root of 5 end fraction

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan fraction numerator square root of 18 plus square root of 5 over denominator square root of 18 minus square root of 5 end fraction dapat dirasionalkan penyebutnya menjadi fraction numerator 23 plus 6 square root of 10 over denominator 13 end fraction.

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 18 plus square root of 5 over denominator square root of 18 minus square root of 5 end fraction sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 18 plus square root of 5 over denominator square root of 18 minus square root of 5 end fraction end cell equals cell fraction numerator square root of 18 plus square root of 5 over denominator square root of 18 minus square root of 5 end fraction cross times fraction numerator square root of 18 plus square root of 5 over denominator square root of 18 plus square root of 5 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 18 plus square root of 5 close parentheses open parentheses square root of 18 plus square root of 5 close parentheses over denominator open parentheses square root of 18 minus square root of 5 close parentheses open parentheses square root of 18 plus square root of 5 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses square root of 18 close parentheses squared plus 2 square root of 18 cross times 5 end root plus open parentheses square root of 5 close parentheses squared over denominator open parentheses square root of 18 close parentheses squared minus open parentheses square root of 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 18 plus 2 square root of 9 cross times 2 cross times 5 end root plus 5 over denominator 18 minus 5 end fraction end cell row blank equals cell fraction numerator 18 plus open parentheses 2 cross times 3 square root of 10 close parentheses plus 5 over denominator 13 end fraction end cell row blank equals cell fraction numerator 23 plus 6 square root of 10 over denominator 13 end fraction end cell end table  

Dengan demikian, pecahan fraction numerator square root of 18 plus square root of 5 over denominator square root of 18 minus square root of 5 end fraction dapat dirasionalkan penyebutnya menjadi fraction numerator 23 plus 6 square root of 10 over denominator 13 end fraction.

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