Question

Given that: $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236\mathrm{and}\sqrt{7}=2.646,$ find the square roots of the following:
(i) $\frac{196}{75}$
(ii) $\frac{400}{63}$
(iii) $\frac{150}{7}$
(iv) $\frac{256}{5}$
(v) $\frac{25}{50}$

Answer 1

From the given values, we can simplify the expressions in the following manner:

$$\begin{gathered} \left(\mathrm{i}\right)\sqrt{\frac{196}{75}}=\frac{14}{5\sqrt{3}}=\frac{14}{5\times 1.732}=1.617 \\ \left(\mathrm{ii}\right)\sqrt{\frac{400}{63}}=\frac{20}{3\sqrt{7}}=\frac{20}{3\times 2.646}=2.520 \\ \left(\mathrm{iii}\right)\sqrt{\frac{150}{7}}=\frac{5\sqrt{2}\times \sqrt{3}}{\sqrt{7}}=\frac{5\times 1.414\times 1.732}{2.646}=4.628 \\ \left(\mathrm{iv}\right)\sqrt{\frac{256}{5}}=\frac{16}{\sqrt{5}}=\frac{16}{2.236}=7.155 \\ \left(\mathrm{v}\right)\sqrt{\frac{27}{50}}=\frac{3\sqrt{3}}{5\sqrt{2}}=\frac{3\times 1.732}{5\times 1.414}=0.735 \end{gathered}$$