Question

The following numbers are obviously not perfect squares. Give reason. 

1. 1057 
2. 23453 
3. 7928 
4. 222222 
5. 64000 
6. 89722 
7. 222000 
8. 505050

Answer 1

The square of numbers may end with any one of the digits \(0, 1, 5, 6\), or \(9\). Also, a perfect square has even number of zeroes at the end of it.
(i) \(1057\) has its unit place digit as \(7\). 
Therefore, it cannot be a perfect square.

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(ii) \(23453\) has its unit place digit as \(3\). 
Therefore, it cannot be a perfect square.

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(iii) \(7928\) has its unit place digit as \(8\). 
Therefore, it cannot be a perfect square.

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(iv) \(222222\) has its unit place digit as \(2\). 
Therefore, it cannot be a perfect square.

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(v) \(64000\) has three zeros at the end of it. 
However, since a perfect square cannot end with odd number of zeroes, it is not a perfect square.

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(vi) \(89722\) has its unit place digit as \(2\). 
Therefore, it cannot be a perfect square.

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(vii) \(222000\) has three zeroes at the end of it. 
However, since a perfect square cannot end with odd number of zeroes, it is not a perfect square.

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(viii) \(505050\) has one zero at the end of it. 
However, since a perfect square cannot end with odd number of zeroes, it is not a perfect square.