Question

Find the number of digits in the square root of $2500$ (without any calculation).

Answer 1

State the formula for number of digits in square root according to given condition and evaluate

Let, $n=$ number of digits in the given number.

When $n$ is even, the number of digits in the square root will be $\frac{n}{2}$.

When $n$ is odd, the number of digits in the square root will be $\frac{n+1}{2}$.

Consider the number $2500$

There are four digits in $2500$ So,

$Numberofdigitsinsquareroot=\frac{n}{2}$

$$\begin{gathered} =\frac{4}{2} \\ =2 \end{gathered}$$

Hence, there are $2$ digits in the square root of $2500$.