Question

The value of $\frac{1}{\sqrt{3.25}+\sqrt{2.25}}+\frac{1}{\sqrt{4.25}+\sqrt{3.25}}$ $+\frac{1}{\sqrt{5.25}+\sqrt{4.25}}+\frac{1}{\sqrt{6.25}+\sqrt{5.25}}$ is

• A. $1.00$
• B. $1.25$
• C. $1.50$
• D. $2.25$

Answer 1

The correct option is A $1.00$

Given $\frac{1}{\sqrt{3.25}+\sqrt{2.25}}+\frac{1}{\sqrt{4.25}+\sqrt{3.25}}$ $+\frac{1}{\sqrt{5.25}+\sqrt{4.25}}+\frac{1}{\sqrt{6.25}+\sqrt{5.25}}$

$\frac{1}{\sqrt{3.25}+\sqrt{2.25}}$$=\frac{(\sqrt{3.25}-\sqrt{2.25})}{(\sqrt{3.25}+\sqrt{2.25}(\sqrt{3.25}-\sqrt{2.25})}$

$=\frac{\sqrt{3.25}-\sqrt{2.25}}{(\sqrt{3.25}{)}^2-(\sqrt{2.25}{)}^2}=\frac{\sqrt{3.25}-\sqrt{2.25}}{3.25-2.25}=\sqrt{3.25}-\sqrt{2.25}$

Simiarly, $\frac{1}{\sqrt{4.25}+\sqrt{3.25}}=\sqrt{4.25}-\sqrt{3.25,}$

$\Rightarrow \frac{1}{\sqrt{5.25}+\sqrt{4.25}}=\sqrt{5.25}-\sqrt{3.25,}$

$\Rightarrow \frac{1}{\sqrt{5.25}+\sqrt{4.25}}=\sqrt{5.25}-\sqrt{4.25}$ and

$\Rightarrow \frac{1}{\sqrt{6.25}+\sqrt{5.25}}=\sqrt{6.25}-\sqrt{5.25}$

$\therefore$ Given exp $=\sqrt{3.25}-\sqrt{2.25}+\sqrt{4.25}-\sqrt{3.25}$$+\sqrt{5.25}-\sqrt{4.25}+\sqrt{6.25}-\sqrt{5.25}$

$=\sqrt{6.25}-\sqrt{2.25}=2.5-1.5=1$