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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

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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

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(i) We know that the unit’s digit of the square of a number having digit as unit’s

place 1 is 1 and also 9 is 1[92 = 81 whose unit place is 1].

∴ Unit’s digit of the square root of number 9801 is equal to 1 or 9.

(ii) We know that the unit’s digit of the square of a number having digit as unit’s

place 6 is 6 and also 4 is 6 [62 = 36 and 42 = 16, both the squares have unit digit 6].

∴ Unit’s digit of the square root of number 99856 is equal to 6.

(iii) We know that the unit’s digit of the square of a number having digit as unit’s

place 1 is 1 and also 9 is 1[92=81 whose unit place is 1].

∴ Unit’s digit of the square root of number 998001 is equal to 1 or 9.

(iv) We know that the unit’s digit of the square of a number having digit as unit’s

place 5 is 5.

∴ Unit’s digit of the square root of number 657666025 is equal to 5.

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