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1. 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

Solution:

\begin{aligned} \frac{1}{\sqrt{3.25} + \sqrt{2.25}} \times \frac{\sqrt{3.25} - \sqrt{2.25}}{\sqrt{3.25} - \sqrt{2.25}} \\ = \frac{\sqrt{3.25} - \sqrt{2.25}}{3.25 - 2.25} \\ = \sqrt{3.25} - \sqrt{2.25} . . . . . . (i) \\ Similarly \\ \frac{1}{\sqrt{4.25} + \sqrt{3.25}} \\ = \sqrt{4.25} - \sqrt{3.25} . . . . . . . (i i) \\ \frac{1}{\sqrt{5.25} + \sqrt{4.25}} \\ = \sqrt{5.25} - \sqrt{4.25} . . . . . . . (i i i) \\ \frac{1}{\sqrt{6.25} + \sqrt{5.25}} \\ = \sqrt{6.25} - \sqrt{5.25} . . . . . . . (i v) \\ Now add all them \\ \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 \end{aligned}

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