Using square root table, find the square root

On prime factorisation:

4955 is equal to $5 \times 991$, which means that $\sqrt{4955}=\sqrt{5} \times \sqrt{11}$.

The square root of 991 is not listed in the table; it lists the square roots of all the numbers below 100.

Hence, we have to manipulate the number such that we get the square root of a number less than 100. This can be done in the following manner:

$\sqrt{4955}=\sqrt{49.55 \times 100}=\sqrt{49.55} \times 10$

Now, we have to find the square root of 49.55.

We have: $\sqrt{49}=7$ and $\sqrt{50}=7.071$.

Their difference is 0.071.

Thus, for the difference of 1 (50 -">− 49), the difference in the values of the square roots is 0.071.

For the difference of 0.55, the difference in the values of the square roots is:

0.55 ×">× 0.0701 = 0.03905

$\therefore \sqrt{49.55}=7+0.03905=7.03905$

Finally, we have:

$\sqrt{4955}=\sqrt{49.55} \times 10=7.03905 \times 10=70.3905$