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What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
(i) 9801 (ii) 99856
(iii) 998001 (iv) 657666025#new_question_
Without doing any calculation, find the numbers which are surely not perfect squares.
(i) 153 (ii) 257
(iii) 408 (iv) 441
Asked by Harsh Last Modified
Answer 
Charlie
(i) If the number ends with 1, then the one’s digit of the square root of that number may be 1 or 9. Therefore, one’s digit of the square root of 9801 is either 1 or 9.
(ii) If the number ends with 6, then the one’s digit of the square root of that number may be 4 or 6. Therefore, one’s digit of the square root of 99856 is either 4 or 6.
(iii) If the number ends with 1, then the one’s digit of the square root of that number may be 1 or 9. Therefore, one’s digit of the square root of 998001 is either 1 or 9.
(iv) If the number ends with 5, then the one’s digit of the square root of that number will be 5. Therefore, the one’s digit of the square root of 65,76,66,025 is 5.
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