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Rasionalkan penyebut pecahan-pecahan berikut! 26​−7​2​​

Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut!

fraction numerator square root of 2 over denominator 2 square root of 6 minus square root of 7 end fraction

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan fraction numerator square root of 2 over denominator 2 square root of 6 minus square root of 7 end fraction dapat dirasionalkan penyebutnya menjadi fraction numerator 4 square root of 3 plus square root of 14 over denominator 17 end fraction.

Pembahasan

Ingat kembali aturan berikut.

  • open parentheses square root of a minus square root of b close parentheses open parentheses square root of a plus square root of b close parentheses equals a minus b 
  • 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 2 over denominator 2 square root of 6 minus square root of 7 end fraction sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 2 over denominator 2 square root of 6 minus square root of 7 end fraction end cell equals cell fraction numerator square root of 2 over denominator 2 square root of 6 minus square root of 7 end fraction cross times fraction numerator 2 square root of 6 plus square root of 7 over denominator 2 square root of 6 plus square root of 7 end fraction end cell row blank equals cell fraction numerator square root of 2 open parentheses 2 square root of 6 plus square root of 7 close parentheses over denominator open parentheses 2 square root of 6 minus square root of 7 close parentheses open parentheses 2 square root of 6 plus square root of 7 close parentheses end fraction end cell row blank equals cell fraction numerator 2 square root of 2 cross times 6 end root plus square root of 2 cross times 7 end root over denominator open parentheses 2 square root of 6 close parentheses squared minus open parentheses square root of 7 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 square root of 12 plus square root of 14 over denominator open parentheses 4 cross times 6 close parentheses minus 7 end fraction end cell row blank equals cell fraction numerator 2 square root of 4 cross times 3 end root plus square root of 14 over denominator 24 minus 7 end fraction end cell row blank equals cell fraction numerator 2 cross times 2 square root of 3 plus square root of 14 over denominator 17 end fraction end cell row blank equals cell fraction numerator 4 square root of 3 plus square root of 14 over denominator 17 end fraction end cell end table  

Dengan demikian, pecahan fraction numerator square root of 2 over denominator 2 square root of 6 minus square root of 7 end fraction dapat dirasionalkan penyebutnya menjadi fraction numerator 4 square root of 3 plus square root of 14 over denominator 17 end fraction.

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