Question

It being given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236\mathrm{and}\sqrt{10}=3.162$, find the value of three places of decimals, of each of the following.
(i) $\frac{2}{\sqrt{5}}$

(ii) $\frac{{\displaystyle 2-\sqrt{3}}}{{\displaystyle \sqrt{3}}}$

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

Answer 1

(i)
$$\begin{gathered} \frac{2}{\sqrt{5}} \\ =\frac{2}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}} \\ =\frac{2\sqrt{5}}{5} \end{gathered}$$
$$\begin{gathered} =\frac{2\times 2.236}{5} \\ =0.894 \end{gathered}$$
(ii)
$$\begin{gathered} \frac{{\displaystyle 2-\sqrt{3}}}{{\displaystyle \sqrt{3}}} \\ =\frac{{\displaystyle 2-\sqrt{3}}}{{\displaystyle \sqrt{3}}}\times \frac{\sqrt{3}}{\sqrt{3}} \\ =\frac{2\sqrt{3}-3}{3} \end{gathered}$$
$$\begin{gathered} =\frac{2\times 1.732-3}{3} \\ =0.155 \end{gathered}$$
(iii)
$$\begin{gathered} \frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}} \\ =\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}} \\ =\frac{\sqrt{2}\left(\sqrt{10}-\sqrt{5}\right)}{2} \end{gathered}$$
$$\begin{gathered} =\frac{1.414\times \left(3.162-2.236\right)}{2} \\ =0.655 \end{gathered}$$