It being given that $\sqrt{2}=1.414, \sqrt{3}=1.732, \sqrt{5}=2.236$ and $\sqrt{10}=3.162$, 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) $\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}$
(i)
$\frac{2}{\sqrt{5}}$
$=\frac{2}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}$
$=\frac{2 \sqrt{5}}{5}$
$=\frac{2 \times 2.236}{5}$
$=0.894$
(ii)
$\frac{2-\sqrt{3}}{\sqrt{3}}$
$=\frac{2-\sqrt{3}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$
$=\frac{2 \sqrt{3}-3}{3}$
$=\frac{2 \times 1.732-3}{3}$
$=0.155$
(iii)
$\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}$
$=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$
$=\frac{\sqrt{2}(\sqrt{10}-\sqrt{5})}{2}$
$=\frac{1.414 \times(3.162-2.236)}{2}$
$=0.655$