Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut! 18 + 3 7

Rasionalkan penyebut pecahan-pecahan berikut!

$\frac{7}{18 + 3}$

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Klaim

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan dapat dirasionalkan penyebutnya menjadi .

pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 7 over denominator square root of 18 plus 3 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 7 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses square root of 2 minus 1 close parentheses 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.

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

Sehingga dapat dirasionalkan penyebut pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 7 over denominator square root of 18 plus 3 end fraction end cell end table$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 7 over denominator square root of 18 plus 3 end fraction end cell equals cell fraction numerator 7 over denominator square root of 18 plus 3 end fraction cross times fraction numerator square root of 18 minus 3 over denominator square root of 18 minus 3 end fraction end cell row blank equals cell fraction numerator 7 open parentheses square root of 18 minus 3 close parentheses over denominator open parentheses square root of 18 plus 3 close parentheses open parentheses square root of 18 minus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 7 square root of 9 cross times 2 end root minus 7 cross times 3 over denominator 18 minus 3 squared end fraction end cell row blank equals cell fraction numerator 7 square root of 3 squared cross times 2 end root minus 21 over denominator 18 minus 9 end fraction end cell row blank equals cell fraction numerator 7 cross times 3 square root of 2 minus 21 over denominator 9 end fraction end cell row blank equals cell fraction numerator 21 square root of 2 minus 21 over denominator 9 end fraction end cell row blank equals cell 21 over 9 open parentheses square root of 2 minus 1 close parentheses end cell row blank equals cell 7 over 3 open parentheses square root of 2 minus 1 close parentheses end cell end table$

Dengan demikian, pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 7 over denominator square root of 18 plus 3 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi .