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Question

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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Solution

We know that, numbers having 2, 3, 7 or 8 at units place are not perfect squares.
That is because:
12=1
22=4
32=9
42=16
52=25
62=36
72=49
82=64
92=81

Also,
102=100
1002=10000

Hence, any perfect square will end with 1, 4, 5, 6, 9 or even number of zeros.

All the given numbers end with either 2, 3, 7, 8 or with odd number of zeros.

Hence, the given numbers are not perfect squares.

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A perfect square always ends in 0,1,4,5,6,9 as last digit
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