Question

What could be the possible 'one's' digits of the square root of each of the following numbers? 

1. 9801 
2. 99856 
3. 998001 
4. 657666025

Answer 1

(i) If the number ends with \(1\), then the one's digit of the square root of that number may be \(1\) or \(9\). 
Therefore, one's digit of the square root of \(9801\) is either \(1\) or \(9\).

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(ii) If the number ends with \(6\), then the one's digit of the square root of that number may be \(4\) or \(6\). 
Therefore, one's digit of the square root of \(99856 \) is either \(4\) or \(6\).

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(iii) If the number ends with \(1\), then the one's digit of the square root of that number may be \(1\) or 9. 
Therefore, one's digit of the square root of \(998001\) is either \(1\) or \(9\).

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(iv) If the number ends with \(5\), then the one's digit of the square root of that number will be \(5\).
Therefore, the one's digit of the square root of \(657666025\) is \(5\).