Tentukan hasil pengurangan dari pecahan berikut! 32−63

Pertanyaan

Tentukan hasil pengurangan dari pecahan berikut!

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

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 over denominator square root of 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 3 over denominator square root of 6 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 6 minus 3 square root of 2 over denominator 6 end fraction end cell end table$ .

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

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 2 over denominator square root of 3 end fraction minus fraction numerator square root of 3 over denominator square root of 6 end fraction end cell equals cell fraction numerator square root of 2 cross times square root of 4 over denominator square root of 12 end fraction minus fraction numerator square root of 3 cross times square root of 2 over denominator square root of 12 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus square root of 6 over denominator square root of 12 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 minus square root of 6 over denominator square root of 12 end fraction cross times fraction numerator square root of 12 over denominator square root of 12 end fraction end cell row blank equals cell fraction numerator 2 square root of 2 cross times 12 end root minus square root of 6 cross times 12 end root over denominator open parentheses square root of 12 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 square root of 24 minus square root of 72 over denominator 12 end fraction end cell row blank equals cell fraction numerator open parentheses 2 cross times 2 square root of 6 close parentheses minus 6 square root of 2 over denominator 12 end fraction end cell row blank equals cell fraction numerator 4 square root of 6 minus 6 square root of 2 over denominator 12 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 3 square root of 2 over denominator 6 end fraction end cell end table$

Dengan demikian, diperoleh $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 over denominator square root of 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 3 over denominator square root of 6 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 square root of 6 minus 3 square root of 2 over denominator 6 end fraction end cell end table$ .