Question

Find the number of digits in the square roots of $1764$.

Answer 1

Compute the required number of digits:

The number $1764$ can be written as

$1764=2x2x3x3x7x7$

$=2^2\times 3^2\times 7^2$

So the square root is

$\sqrt{1764}=\sqrt{2^2\times 3^2\times 7^2}$

$$\begin{gathered} =2\times 3\times 7 \\ =42 \end{gathered}$$

Hence, the number of digits in the square root of $1764$ is $2$.