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Pertanyaan

Tentukan hasil pengurangan dari pecahan berikut!

 

fraction numerator 2 over denominator square root of 6 end fraction minus fraction numerator square root of 6 over denominator 2 square root of 3 end fraction

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh fraction numerator 2 over denominator square root of 6 end fraction minus fraction numerator square root of 6 over denominator 2 square root of 3 end fraction equals fraction numerator 2 square root of 6 minus 3 square root of 2 over denominator 6 end fraction.

Pembahasan

Untuk merasionalkan penyebut pecahan berbentuk fraction numerator a over denominator square root of b end fraction dapat dilakukan dengan rumus dan prosedur sebagai berikut.

fraction numerator a over denominator square root of b end fraction equals fraction numerator a over denominator square root of b end fraction cross times fraction numerator square root of b over denominator square root of b end fraction

Sehingga pengurangan pecahan  fraction numerator 2 over denominator square root of 6 end fraction minus fraction numerator square root of 6 over denominator 2 square root of 3 end fraction dapat ditentukan hasilnya dengan terlebih dahulu menyamakan penyebutnya, kemudian dilakukan rasionalisasi penyebut pecahan, seperti ditunjukkan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 over denominator square root of 6 end fraction minus fraction numerator square root of 6 over denominator 2 square root of 3 end fraction end cell equals cell fraction numerator 2 cross times square root of 2 over denominator square root of 12 end fraction minus fraction numerator square root of 6 over denominator square root of 12 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus square root of 6 over denominator square root of 12 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus square root of 6 over denominator 2 square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 cross times 3 end root minus square root of 6 cross times 3 end root over denominator 2 open parentheses square root of 3 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus square root of 18 over denominator 2 cross times 3 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 3 square root of 2 over denominator 6 end fraction end cell end table 

Dengan demikian, diperoleh fraction numerator 2 over denominator square root of 6 end fraction minus fraction numerator square root of 6 over denominator 2 square root of 3 end fraction equals fraction numerator 2 square root of 6 minus 3 square root of 2 over denominator 6 end fraction.

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