Question

Find the number of digits in the square root of each of the following numbers (without any calculation).

1. 64
2. 144
3. 4489
4. 27225
5. 390625

Answer 1

(i) By placing bars, we obtain
$64=\bar{64}$
Since there is only one bar, the square root of $64$ will have only one digit in it.

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(ii) By placing bars, we obtain
$144=\bar1 \bar{44}$
Since there are two bars, the square root of $144$ will have $2$ digits in it.

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(iii) By placing bars, we obtain
$4489=\bar{44}\bar{ 89}$
Since there are two bars, the square root of $4489$ will have $2$ digits in it.

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(iv) By placing bars, we obtain
$27225 = \bar2 \,\bar{72} \,\bar{25}$
Since there are three bars, the square root of $27225$ will have three digits in it.

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(v) By placing the bars, we obtain
$390625= \bar{39} \;\bar{06}\; \bar{25}$
Since there are three bars, the square root of $390625$ will have $3$ digits in it.