Question

Simplify: $\frac{3+\sqrt{6}}{5\sqrt{3}-2\sqrt{12}-\sqrt{32}+\sqrt{50}}$

• A. $3\sqrt{2}$
• B. $3$
• C. $6$
• D. $\sqrt{3}$

Answer 1

The correct option is D $\sqrt{3}$

$\frac{3+\sqrt{6}}{5\sqrt{3}-2\sqrt{12}-\sqrt{32}+\sqrt{50}}$

$\Rightarrow \frac{3+\sqrt{6}}{5\sqrt{3}-2\sqrt{4\times 3}-\sqrt{16\times 2}+\sqrt{25\times 2}}$

$\Rightarrow \frac{3+\sqrt{6}}{5\sqrt{3}-4\sqrt{3}-4\sqrt{2}+5\sqrt{2}}$

$\Rightarrow \frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}$

Now multiplying and divide by $\sqrt{3}-\sqrt{2}$,

$\Rightarrow \frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

$\Rightarrow \frac{3\sqrt{3}+\sqrt{18}-3\sqrt{2}-\sqrt{12}}{3-2}$

$\Rightarrow \frac{3\sqrt{3}+\sqrt{9\times 2}-3\sqrt{2}-\sqrt{4\times 3}}{1}$

$\Rightarrow 3\sqrt{3}+3\sqrt{2}-3\sqrt{2}-2\sqrt{3}$

$\Rightarrow 3\sqrt{3}-2\sqrt{3}$

$\Rightarrow \sqrt{3}(3-2)$

$\Rightarrow \sqrt{3}$