Question

Simplify: $\frac{1}{(5-2\sqrt{3})}.$

• A. $$\frac{(5-2\sqrt{3})}{16}$$
• B. $$\frac{(5+2\sqrt{3})}{13}$$
• C. $$\frac{(5-2\sqrt{3})}{14}$$
• D. $$\frac{(5+2\sqrt{3})}{12}$$

Answer 1

Answer:

$$\frac{(5+2\sqrt{3})}{13}$$

Solution:

On rationalization of $\frac{1}{(5-2\sqrt{3})}$.

$= \frac{1}{(5-2\sqrt{3})}\times{\frac{(5 +2\sqrt{3})}{(5 + 2\sqrt{3})}}$

$=\frac {(5 + 2\sqrt{3})}{(25-12)}$

$=\frac {(5 + 2\sqrt{3})}{13}$