Question

Find the number of digits in the square root of each of the following numbers (without any calculation).
(i) $64$ (ii) $144$ (iii) $4489$ (iv) $27225$ (v) $390625$

Answer 1

(i) No. of digits in the square root.

If (N) is the number of digits of given number

N$=$even $=\frac{N}{2}$(no. of digits in square root)

N$=$odd $=\frac{N+1}{2}$( no. of digits in square root)

(i) $64$

Here, $N=2$ (even)

$\Rightarrow \frac{N}{2}=\frac{2}{2}=1$ digit

(ii) $144$

Here, $N=3$ (odd)

$\Rightarrow \frac{N+1}{2}=\frac{3+1}{2}=\frac{4}{2}=2$ digits

(iii) $4489$

Here, $N=4$ (even)

$\Rightarrow \frac{N}{2}=\frac{4}{2}=2$ digits

(iv) $27225$

Here, $N=5$ (even)

$\Rightarrow \frac{N+1}{2}=\frac{5+1}{2}=3$ digits

(v) $390625$

Here, $N=6$ (even)

$\Rightarrow \frac{N}{2}=\frac{6}{2}=3$ digits