Question

Find $\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}$

• A. $2$
• B. $7$
• C. $3$
• D. $5$

Answer 1

The correct option is D $5$

Given:
$\Rightarrow \frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}+\frac{1}{\sqrt{5}-2}-\frac{1}{\sqrt{6}-\sqrt{5}}$

Rationalizing above terms we get:
$=3+\sqrt{8}-\sqrt{8}-\sqrt{7}+\sqrt{7}+\sqrt{6}+\sqrt{5}+2-\sqrt{6}-\sqrt{5}$

$3+2$

$=5$

So, option (c) is correct.