Pertanyaan

3 + 2 2 3 2 = ...

$\frac{3 2}{3 + 2 2} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

rasionalisasi bentuk adalah .

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

Pembahasan

Perhatikan perhitungan berikut. Ingat, rasionalisasi bentuk akar: b + c d a = b + c d a × b − c d b − c d Maka: Jadi, rasionalisasi bentuk adalah .

Perhatikan perhitungan berikut.

Ingat, rasionalisasi bentuk akar:

$\frac{a}{b + c d} = \frac{a}{b + c d} \times \frac{b - c d}{b - c d}$

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 .