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
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
(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[9^{2 }= 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 [6^{2 }= 36 and 4^{2 }= 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[9^{2}=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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