Question

# It being given that , find the value of three places of decimals, of each of the following. (i) $\frac{2}{\sqrt{5}}$ (ii) $\frac{2-\sqrt{3}}{\sqrt{3}}$ (iii) $\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}$

Solution

## (i)  $\frac{2}{\sqrt{5}}\phantom{\rule{0ex}{0ex}}=\frac{2}{\sqrt{5}}×\frac{\sqrt{5}}{\sqrt{5}}\phantom{\rule{0ex}{0ex}}=\frac{2\sqrt{5}}{5}$ $=\frac{2×2.236}{5}\phantom{\rule{0ex}{0ex}}=0.894$ (ii)  $\frac{2-\sqrt{3}}{\sqrt{3}}\phantom{\rule{0ex}{0ex}}=\frac{2-\sqrt{3}}{\sqrt{3}}×\frac{\sqrt{3}}{\sqrt{3}}\phantom{\rule{0ex}{0ex}}=\frac{2\sqrt{3}-3}{3}$ $=\frac{2×1.732-3}{3}\phantom{\rule{0ex}{0ex}}=0.155$ (iii)  $\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}\phantom{\rule{0ex}{0ex}}=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}×\frac{\sqrt{2}}{\sqrt{2}}\phantom{\rule{0ex}{0ex}}=\frac{\sqrt{2}\left(\sqrt{10}-\sqrt{5}\right)}{2}$ $=\frac{1.414×\left(3.162-2.236\right)}{2}\phantom{\rule{0ex}{0ex}}=0.655$MathematicsRS Aggarwal (2020, 2021)All

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