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soal-merasionalkan-penyebut-pecahan-bentuk-akar

Soal Merasionalkan Penyebut Pecahan Bentuk Akar

Soal
Bentuk sederhana dari $\frac{(\sqrt{3}+\sqrt{7})(\sqrt{3}-\sqrt{7})}{2\sqrt{5}-4\sqrt{2}}$ adalah …
Jawaban \begin{align} \frac{(\sqrt{3}+\sqrt{7})(\sqrt{3}-\sqrt{7})}{2\sqrt{5}-4\sqrt{2}} &= \frac{3-7}{2\sqrt{5}-4\sqrt{2}}\times\frac{2\sqrt{5}+4\sqrt{2}}{2\sqrt{5}+4\sqrt{2}}\\ &=\frac{-4(2\sqrt{5}+4\sqrt{2})}{20-32}\\ &=\frac{-8(\sqrt{5}+2\sqrt{2})}{-12}\\ &=-\frac{2}{3}(\sqrt{5}+2\sqrt{2}) \end{align}


Soal
Hasil dari $\frac{(1+\sqrt7)(1-\sqrt7)}{2+\sqrt5}$ adalah…

A. $12+6\sqrt5$
B. $12+\sqrt5$
C. $-12+6\sqrt5$
D. $12-6\sqrt5$
E. $-12+\sqrt5$

Jawaban: D

Proses penyelesaian \begin{align*} \frac{(1+\sqrt7)(1-\sqrt7)}{2+\sqrt5}&=\frac{1-7}{2+\sqrt5}\\ &=\frac{-6}{2+\sqrt5}\times\frac{2+\sqrt5}{2+\sqrt5}\\ &=\frac{-12+6\sqrt5}{4-5}\\ &=12-6\sqrt5 \end{align*}

soal-merasionalkan-penyebut-pecahan-bentuk-akar.txt · Last modified: 07/04/2018 11:06 by Sopandi Ahmad