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Pertanyaan

Rasionalkan penyebut bentuk-bentuk akar berikut.

a. fraction numerator 2 minus square root of 2 over denominator square root of 2 end fraction 

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

diperoleh fraction numerator 2 minus square root of 2 over denominator square root of 2 end fraction equals square root of 2 minus 1.

Pembahasan

Ingat kembali cara merasionalkan pecahan dengan penyebut bentuk akar.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator 2 minus square root of 2 over denominator square root of 2 end fraction end cell equals cell fraction numerator 2 minus square root of 2 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus square root of 2 cross times 2 end root over denominator square root of 2 cross times 2 end root end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus square root of 4 over denominator square root of 4 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus 2 over denominator 2 end fraction end cell row blank equals cell square root of 2 minus 1 end cell end table

Jadi, diperoleh fraction numerator 2 minus square root of 2 over denominator square root of 2 end fraction equals square root of 2 minus 1.

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