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Question:

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

Solution:

(i) 9801
Observe that the numbers ending with 1 and 9 are the only numbers whose square numbers end with 1. 1²=1 and 9²=81
Since the last digit of 9801 is 1, the possible one's digit of its square root can be 1 or 9.
(ii) 99856
Observe that the numbers ending with 4 and 6 are the only numbers whose square numbers end with 6. 4²=16 and 6²=36
Since the last digit of 99856 is 6, the possible one's digit of its square root can be 4 or 6.
(iii) 998001
Observe that the numbers ending with 1 and 9 are the only numbers whose square numbers end with 1. 1²=1 and 9²=81
Since the last digit of 998001 is 1, the possible one's digit of its square root can be 1 or 9.
(iv) 657666025
Observe that the numbers ending with 5 are the only numbers whose square numbers end with 25. 5²=25
Since the last two digits of 657666025 are 25, the possible one's digit of its square root can be 5.