Question

Find the square root of $10\frac{2}{3}$ correct to two places of decimal

Answer 1

Given number: $10\frac{2}{3}$

$10\frac{2}{3}=\frac{32}{3}=10.666666.....$
In order to find the square root correct to two places of decimal, we have to find the square root up to three places. Therefore, we have to convert $10\frac{2}{3}$ as a decimal correct to six places.
Now, lets evaluate the $\sqrt{\mathrm{10.66666......}}$

Which we rounded to $\sqrt{10.666667}$

From the table,$\sqrt{10.666667}=3.265$(approximately)

$\Rightarrow \sqrt{10\frac{2}{3}}=3.27$ (correct to two places of decimal)