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SMK Teknologi dan Rekayasa

Soal 11 Pecahan Bentuk Akar


Bentuk\ sederhana\ dari\ \frac{2\sqrt{3}}{2-\sqrt{3}}\ adalah\ ....\\\\a.\ \ 4\sqrt{3}-\sqrt{6}\ \ \ \ \ \ b.\ \ 4\sqrt{3}+\sqrt{6}\ \ \ \ \ \ c.\ \ 1\ \ \ \ \ \ d.\ \ 2+\sqrt{3}\ \ \ \ \ \ e.\ \ 6\sqrt{3}-4
Jawaban: b

\begin{array}{rcl}\frac{2\sqrt{3}}{2-\sqrt{3}}&=&\frac{2\sqrt{3}}{2-\sqrt{3}}\ \times \ \frac{2+\sqrt{3}}{2+\sqrt{3}}\\\\&=&\frac{2\sqrt{3}(2+\sqrt{3})}{2^{2}-(\sqrt{3})^{2}}\\\\&=&\frac{4\sqrt{3}+2.3}{4-3}\\\\&=&\frac{4\sqrt{3}+6}{1}\\\\&=&4\sqrt{3}+6\end{array}

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