Using square root table, find the square root

We have to find $\sqrt{21.97}$.

From the square root table, we have:

$\sqrt{21}=\sqrt{3} \times \sqrt{7}=4.583$ and $\sqrt{22}=\sqrt{2} \times \sqrt{11}=4.690$

Their difference is 0.107.

Thus, for the difference of 1 (22 -">−21), the difference in the values of the square roots is 0.107.

For the difference of 0.97, the difference in the values of their square roots is:

$0.107 \times 0.97=0.104$

$\therefore \sqrt{21.97}=4.583+0.104 \approx 4.687$