Question

Solve the following:

$\frac{2}{\sqrt{5}+\sqrt{3}}+\frac{7}{\sqrt{5}-\sqrt{3}}$ .

• A. $14$
• B. $14.39$
• C. $14.392$
• D. $16$

Answer 1

The correct option is C $14.392$

$\frac{2}{\sqrt{5}+\sqrt{3}}+\frac{7}{\sqrt{5}-\sqrt{3}}$

$=$ $\frac{2\sqrt{5}-2\sqrt{3}+7\sqrt{5}+7\sqrt{3}}{5-3}$ $=$ $\frac{9\sqrt{5}+5\sqrt{3}}{2}$.

(Substitute values of $\sqrt{5}=2.237$ and $\sqrt{3}=1.732$)
$=$ $\frac{9\times 2.237+1.732\times 5}{2}$ $=$ $14.392$.

Therefore, option $C$ is correct.