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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

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.