Rasionalkan setiap bentuk akar berikut. d). 5​−3​6​

Pertanyaan

Rasionalkan setiap bentuk akar berikut.

d). begin mathsize 14px style fraction numerator 6 over denominator square root of 5 minus square root of 3 end fraction end style 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah begin mathsize 14px style 3 open parentheses square root of 5 plus square root of 3 close parentheses end style.

Pembahasan

Ingat:

begin mathsize 14px style 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 equals fraction numerator square root of a plus square root of b over denominator a minus b end fraction end style

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 6 over denominator square root of 5 minus square root of 3 end fraction end cell equals cell fraction numerator 6 over denominator square root of 5 minus square root of 3 end fraction cross times fraction numerator square root of 5 plus square root of 3 over denominator square root of 5 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator open parentheses square root of 5 minus square root of 3 close parentheses open parentheses square root of 5 plus square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator 5 minus 3 end fraction end cell row blank equals cell fraction numerator 6 open parentheses square root of 5 plus square root of 3 close parentheses over denominator 2 end fraction end cell row blank equals cell 3 open parentheses square root of 5 plus square root of 3 close parentheses end cell end table end style

Jadi, jawaban yang tepat adalah begin mathsize 14px style 3 open parentheses square root of 5 plus square root of 3 close parentheses end style.

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