# find the square roots of the following:

Question:

Given that: $\sqrt{2}=1.414, \sqrt{3}=1.732, \sqrt{5}=2.236$ and $\sqrt{7}=2.646$, find the square roots of the following:

(i) $\sqrt{\frac{196}{75}}=\frac{14}{5 \sqrt{3}}=\frac{14}{5 \times 1.732}=1.617$

(ii) $\sqrt{\frac{400}{63}}=\frac{20}{3 \sqrt{7}}=\frac{20}{3 \times 2.646}=2.520$

(iii) $\sqrt{\frac{150}{7}}=\frac{5 \sqrt{2} \times \sqrt{3}}{\sqrt{7}}=\frac{5 \times 1.414 \times 1.732}{2.646}=4.628$

(iv) $\sqrt{\frac{256}{5}}=\frac{16}{\sqrt{5}}=\frac{16}{2.236}=7.155$

$(\mathrm{v}) \sqrt{\frac{27}{50}}=\frac{3 \sqrt{3}}{5 \sqrt{2}}=\frac{3 \times 1.732}{5 \times 1.414}=0.735$

Solution:

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

(i) $\sqrt{\frac{196}{75}}=\frac{14}{5 \sqrt{3}}=\frac{14}{5 \times 1.732}=1.617$

(ii) $\sqrt{\frac{400}{63}}=\frac{20}{3 \sqrt{7}}=\frac{20}{3 \times 2.646}=2.520$

(iii) $\sqrt{\frac{150}{7}}=\frac{5 \sqrt{2} \times \sqrt{3}}{\sqrt{7}}=\frac{5 \times 1.414 \times 1.732}{2.646}=4.628$

(iv) $\sqrt{\frac{256}{5}}=\frac{16}{\sqrt{5}}=\frac{16}{2.236}=7.155$

(v) $\sqrt{\frac{27}{50}}=\frac{3 \sqrt{3}}{5 \sqrt{2}}=\frac{3 \times 1.732}{5 \times 1.414}=0.735$