# It being given that

Question:

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) $\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}$

Solution:

(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)

$\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}$

$=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$=\frac{\sqrt{2}(\sqrt{10}-\sqrt{5})}{2}$

$=\frac{1.414 \times(3.162-2.236)}{2}$

$=0.655$