Pertanyaan

Hasil dari 12 4 + 27 1 − 3 1 + 48 1 adalah ....

Hasil dari $\frac{4}{12} + \frac{1}{27} - \frac{1}{3} + \frac{1}{48}$ adalah $....$

$fraction numerator 19 square root of 3 over denominator 36 end fraction$
$fraction numerator 5 square root of 3 over denominator 36 end fraction$
$fraction numerator 7 square root of 3 over denominator 20 end fraction$
$fraction numerator 5 square root of 3 over denominator 20 end fraction$

F. Kartikasari

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Cara merasionalkan penyebut pecahan bentuk akar. Kemudian kita rasionalkan terlebih dahulu setiap pecahannya. Variabel pada bentuk akar dapat dijumlahkan atau dikurangkan jika sejenis dan memenuhi sifat seperti berikut. Jika dan , maka Maka, Oleh karena itu, jawaban yang tepat adalah A.

Cara merasionalkan penyebut pecahan bentuk akar.

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

Kemudian kita rasionalkan terlebih dahulu setiap pecahannya.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 4 over denominator square root of 12 end fraction end cell equals cell fraction numerator 4 over denominator square root of 4 times 3 end root end fraction end cell row blank equals cell fraction numerator 4 over denominator 2 square root of 3 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 2 square root of 3 over denominator 3 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 27 end fraction end cell equals cell fraction numerator 1 over denominator square root of 9 times 3 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator 3 square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator square root of 3 over denominator 9 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 3 end fraction end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator square root of 3 over denominator 3 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 48 end fraction end cell equals cell fraction numerator 1 over denominator square root of 16 times 3 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator 4 square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator square root of 3 over denominator 12 end fraction end cell end table$

Variabel pada bentuk akar dapat dijumlahkan atau dikurangkan jika sejenis dan memenuhi sifat seperti berikut.

Jika p space dan space q element of R dan a greater or equal than 0 , maka

table attributes columnalign right center left columnspacing 0px end attributes row cell p square root of a plus q square root of a end cell equals cell open parentheses p plus q close parentheses square root of a end cell row cell p square root of a minus q square root of a end cell equals cell open parentheses p minus q close parentheses square root of a end cell end table

Maka,

$fraction numerator 4 over denominator square root of 12 end fraction plus fraction numerator 1 over denominator square root of 27 end fraction minus fraction numerator 1 over denominator square root of 3 end fraction plus fraction numerator 1 over denominator square root of 48 end fraction equals fraction numerator 2 square root of 3 over denominator 3 end fraction plus fraction numerator square root of 3 over denominator 9 end fraction minus fraction numerator square root of 3 over denominator 3 end fraction plus fraction numerator square root of 3 over denominator 12 end fraction equals fraction numerator 12 times 2 square root of 3 plus 4 times square root of 3 minus 12 times square root of 3 plus 3 times square root of 3 over denominator 36 end fraction equals fraction numerator 24 square root of 3 plus 4 square root of 3 minus 12 square root of 3 plus 3 square root of 3 over denominator 36 end fraction equals fraction numerator 19 square root of 3 over denominator 36 end fraction$

Oleh karena itu, jawaban yang tepat adalah A.