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1. Given that $\sqrt{5}$ = 2.236 and $\sqrt{3}$ = 1.732, then the value of $\frac{1}{\sqrt{5} + \sqrt{3}} is = ?$

A. 0.564

B. 0.504

C. 0.252

D. 0.202

Solution:

\begin{aligned} \frac{1}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} \\ = \frac{\sqrt{5} - \sqrt{3}}{5 - 3} \\ = \frac{2.236 - 1.732}{2} \\ = \frac{0.504}{2} \\ = 0.252 \end{aligned}

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