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Q.

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

(i) 1057 (ii) 23453 (iii) 7928 

(iv) 222222 (v) 64000 (vi) 89722 

(vii) 222000 (viii) 505050

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Detailed Solution

We know that a perfect square ends with 0, 1, 4, 5, 6, or 9 and they can only have an even number of zeroes at the end.

(i) 1057 

Here the number ends with 7 at its unit place. Hence 1057 is not a perfect square.

(ii) 23453 

Here the number ends with 3 at its unit place. Hence 23453 is not a perfect square.

(iii) 7928 

Here the number ends with 8 at its unit place. Hence 7928 is not a perfect square.

(iv) 222222 

Here the number ends with 2 at its unit place. Hence 222222 is not a perfect square.

(v) 64000 

Here the number ends with 0 but, the perfect square cannot end with an odd number of zero. Hence 64000 is not a perfect square. 

(vi) 89722.

Here the number ends with 2 at its unit place. Hence 89722 is not a perfect square.

(vii) 222000

Here the number ends with 0 but, the perfect square cannot end with an odd number of zero. Hence 222000 is not a perfect square. 

 (viii) 505050

Here the number ends with 0 but, the perfect square cannot end with an odd number of zero. Hence 505050 is not a perfect square. 

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