Question

Find the number of digits in the square root of each of the following number.
$\left(i\right)64$ $\left(ii\right)144$ $\left(iii\right)4489$ $\left(iv\right)27225$ $\left(v\right)390625$

Answer 1

If the number of digits of a number is even, then its square root will have half (whole number) of the number of digits.

If the number of digits of a number are odd, then its square root will have half (nearest greater whole number) of the number of digits.

i) $\sqrt{64}$

The number of digits is 2 i.e. even.

Therefore, there is only 1 digit in the square root of $64$.

ii) $\sqrt{144}$

The number of digits is 3 i.e. odd.

Therefore, there are (1.5 =) 2 digits in the square root of $144$.

iii) $\sqrt{4489}$

The number of digits is 4 i.e. even.

Therefore, there are 2 digits in the square root of $4489$.

iv) $\sqrt{27225}$

The number of digits is 5 i.e. odd.

Therefore, there are (2.5=) 3 digits in the square root of $27225$.

v) $\sqrt{390625}$

The number of digits is 6 i.e. even.

Therefore, there are 3 digits in the square root of $390625$.