Pertanyaan

Rasionalkan penyebut pecahan-pecachan berikut! 8 3 − 4

Rasionalkan penyebut pecahan-pecachan berikut!

$\frac{3 - 4}{8}$

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Habis dalam

Klaim

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

hasil dari merasionalkan adalah .

hasil dari merasionalkan $fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 6 minus 4 square root of 2 over denominator 4 end fraction end cell end table$ .

Pembahasan

Ingat kembali aturan berikut. Bentuk akar dapat dirasionalkan dengan cara Dari rumus di atas, diperoleh perhitungan sebagai berikut. Jadi, hasil dari merasionalkan adalah .

Ingat kembali aturan berikut.

Bentuk akar $fraction numerator square root of a over denominator square root of b end fraction$ dapat dirasionalkan dengan cara $fraction numerator square root of a over denominator square root of b end fraction cross times fraction numerator square root of b over denominator square root of b end fraction$

Dari rumus di atas, diperoleh perhitungan sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction end cell equals cell fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction cross times fraction numerator square root of 8 over denominator square root of 8 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 3 minus 4 close parentheses cross times square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 3 cross times square root of 8 minus 4 cross times square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 3 cross times 8 end root minus 4 square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 24 minus 4 square root of 8 over denominator 8 end fraction end cell row blank equals cell fraction numerator square root of 2 squared cross times 6 end root minus 4 square root of 2 squared cross times 2 end root over denominator 8 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 4 cross times 2 square root of 2 over denominator 8 end fraction end cell row blank equals cell fraction numerator 2 square root of 6 minus 8 square root of 2 over denominator 8 end fraction end cell row blank equals cell fraction numerator up diagonal strike 2 to the power of 1 cross times open parentheses square root of 6 minus 4 square root of 2 close parentheses over denominator up diagonal strike 8 to the power of 4 end fraction end cell row blank equals cell fraction numerator square root of 6 minus 4 square root of 2 over denominator 4 end fraction end cell end table$

Jadi, hasil dari merasionalkan $fraction numerator square root of 3 minus 4 over denominator square root of 8 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 6 minus 4 square root of 2 over denominator 4 end fraction end cell end table$ .