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.