Question

$\frac{\sqrt{2}(2+\sqrt{3})}{\sqrt{3}(\sqrt{3}+1)}\times \frac{\sqrt{2}(2-\sqrt{3})}{\sqrt{3}\left(\sqrt{3-1}\right)}$ is equal to

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{\sqrt{2}}{3}$
• D. $3\sqrt{2}$

Answer 1

The correct option is A $\frac{1}{3}$

Given exp. $=\frac{(\sqrt{2}{)}^2\times (2+\sqrt{3}\left)\right(2-\sqrt{3})}{(\sqrt{3}{)}^2\times (\sqrt{3}+1\left)\right(\sqrt{3}-1)}$
$=\frac{2\times \left[\right(2{)}^2-\left(\sqrt{3}{)}^2\right]}{3\times [{\left(\sqrt{3}\right)}^2-1^2]}=\frac{2\times (4-3)}{3\times (3-1)}$
$=\frac{2\times 1}{3\times 2}=\frac{1}{3}$