Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut! 6 + 4 8 18

Rasionalkan penyebut pecahan-pecahan berikut!

$\frac{18}{6 + 4 8}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan dapat dirasionalkan penyebutnya menjadi .

pecahan $fraction numerator 18 over denominator 6 plus 4 square root of 8 end fraction$ dapat dirasionalkan penyebutnya menjadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 36 square root of 2 minus 27 over denominator 23 end fraction end cell end table$ .

Pembahasan

Ingat kembali aturan berikut. Sehingga dapat dirasionalkan penyebut pecahan sebagai berikut. Dengan demikian, pecahan dapat dirasionalkan penyebutnya menjadi .

Ingat kembali aturan berikut.

$fraction numerator 1 over denominator a plus square root of b end fraction equals fraction numerator 1 over denominator a plus square root of b end fraction cross times fraction numerator a minus square root of b over denominator a minus square root of b end fraction$

Sehingga dapat dirasionalkan penyebut pecahan $fraction numerator 18 over denominator 6 plus 4 square root of 8 end fraction$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 18 over denominator 6 plus 4 square root of 8 end fraction end cell equals cell fraction numerator 18 over denominator 6 plus 4 square root of 8 end fraction cross times fraction numerator 6 minus 4 square root of 8 over denominator 6 minus 4 square root of 8 end fraction end cell row blank equals cell fraction numerator 18 open parentheses 6 minus 4 square root of 4 cross times 2 end root close parentheses over denominator 6 squared minus open parentheses 4 square root of 8 close parentheses squared end fraction end cell row blank equals cell fraction numerator 18 cross times 6 minus 18 cross times 4 cross times 2 square root of 2 over denominator 36 minus 16 cross times 8 end fraction end cell row blank equals cell fraction numerator 108 minus 144 square root of 2 over denominator 36 minus 128 end fraction end cell row blank equals cell fraction numerator 108 minus 144 square root of 2 over denominator negative 92 end fraction end cell row blank equals cell fraction numerator up diagonal strike negative 4 end strike open parentheses negative 27 plus 36 square root of 2 close parentheses over denominator up diagonal strike negative 4 end strike cross times 23 end fraction end cell row blank equals cell fraction numerator negative 27 plus 36 square root of 2 over denominator 23 end fraction end cell row blank equals cell fraction numerator 36 square root of 2 minus 27 over denominator 23 end fraction end cell end table$

Dengan demikian, pecahan $fraction numerator 18 over denominator 6 plus 4 square root of 8 end fraction$ dapat dirasionalkan penyebutnya menjadi $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 36 square root of 2 minus 27 over denominator 23 end fraction end cell end table$ .