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begin mathsize 14px style fraction numerator 3 square root of 2 over denominator 3 plus 2 square root of 2 end fraction equals... end style

Jawaban:

Perhatikan perhitungan berikut.

Ingat, rasionalisasi bentuk akar:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of a plus square root of b end fraction end cell equals cell fraction numerator 1 over denominator square root of a plus square root of b end fraction cross times fraction numerator square root of a minus square root of b over denominator square root of a minus square root of b end fraction end cell end table end style

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 square root of 2 over denominator 3 plus 2 square root of 2 end fraction end cell equals cell fraction numerator 3 square root of 2 over denominator 3 plus 2 square root of 2 end fraction cross times fraction numerator 3 minus 2 square root of 2 over denominator 3 minus 2 square root of 2 end fraction end cell row blank equals cell fraction numerator open parentheses 3 square root of 2 close parentheses open parentheses 3 minus 2 square root of 2 close parentheses over denominator open parentheses 3 plus 2 square root of 2 close parentheses open parentheses 3 minus 2 square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator 9 square root of 2 minus open parentheses 6 times 2 close parentheses over denominator 9 minus open parentheses 4 times 2 close parentheses end fraction end cell row blank equals cell fraction numerator 9 square root of 2 minus 12 over denominator 9 minus 8 end fraction end cell row blank equals cell fraction numerator 9 square root of 2 minus 12 over denominator 1 end fraction end cell row blank equals cell 9 square root of 2 minus 12 end cell end table end style

Jadi, rasionalisasi bentuk begin mathsize 14px style fraction numerator 3 square root of 2 over denominator 3 plus 2 square root of 2 end fraction end style adalah begin mathsize 14px style 9 square root of 12 minus 12 end style.

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