Question

The value of the expression
$\sqrt{\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}+.............upto99terms}$
is equal to :

• A. 9
• B. 3
• C. 1
• D. 0

Answer 1

The correct option is B 3

$\sqrt{\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}+.............upto99terms}$
Rationalizing individual terms,
= $\sqrt{\frac{\sqrt{2}-1}{1}+\frac{\sqrt{3}-\sqrt{2}}{1}+\frac{\sqrt{4}-\sqrt{3}}{1}+.............upto99terms}$
= $\sqrt{\sqrt{100}-1}$
= $\sqrt{10-1}$
= $\sqrt{9}=3$