Rasionalkan penyebut pecahan-pecahan berikut! 23−215+25

Pertanyaan

Rasionalkan penyebut pecahan-pecahan berikut!

$fraction numerator square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi 3 over 5 square root of 5 plus square root of 3 plus 1 over 10 square root of 30 plus 1 half square root of 2

3 over 5 square root of 5 plus square root of 3 plus 1 over 10 square root of 30 plus 1 half square root of 2

Pembahasan

Untuk merasionalkan penyebut pecahan berbentuk $fraction numerator 1 over denominator square root of a minus square root of b end fraction$ dapat dilakukan dengan rumus dan prosedur sebagai berikut.

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

Sehingga dapat dirasionalkan penyebut pecahan $fraction numerator square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction end cell equals cell fraction numerator square root of 15 plus 5 over denominator 2 square root of 3 minus square root of 2 end fraction cross times fraction numerator 2 square root of 3 plus square root of 2 over denominator 2 square root of 3 plus square root of 2 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 15 plus 5 close parentheses open parentheses 2 square root of 3 plus square root of 2 close parentheses over denominator open parentheses 2 square root of 3 minus square root of 2 close parentheses open parentheses 2 square root of 3 plus square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator 2 square root of 15 cross times 3 end root plus 10 square root of 3 plus square root of 15 cross times 2 end root plus 5 square root of 2 over denominator open parentheses 2 square root of 3 close parentheses squared minus open parentheses square root of 2 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 square root of 45 plus 10 square root of 3 plus square root of 30 plus 5 square root of 2 over denominator 12 minus 2 end fraction end cell row blank equals cell fraction numerator open parentheses 2 cross times 3 square root of 5 close parentheses plus 10 square root of 3 plus square root of 30 plus 5 square root of 2 over denominator 10 end fraction end cell row blank equals cell fraction numerator 6 square root of 5 plus 10 square root of 3 plus square root of 30 plus 5 square root of 2 over denominator 10 end fraction end cell row blank equals cell 3 over 5 square root of 5 plus square root of 3 plus 1 over 10 square root of 30 plus 1 half square root of 2 end cell end table$

Dengan demikian, pecahan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 15 plus square root of 25 over denominator 2 square root of 3 minus square root of 2 end fraction end cell end table$ dapat dirasionalkan penyebutnya menjadi 3 over 5 square root of 5 plus square root of 3 plus 1 over 10 square root of 30 plus 1 half square root of 2 .