Question

1. What would be the possible ones digit of the square root of each of the following natural numbers? (Note explain in step by step method)

(i) 6561
(ii) 24336
(iii) 16129
(iv) 160801​

Answer 1

if a number has 1 or 9 in the unit’s place, then it’s square ends in 1.

when a square number ends in 6, the number whose square it is, will have either 4 or 6 in unit’s place

when a square number ends in 9, the number whose square it is, will have either 3 or 7 in unit’s place

when a square number ends in5, the number whose square it is, will have 5 in unit’s place

when a square number ends in 4, the number whose square it is, will have either 2 or 8 in unit’s place

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Solution:

1) 1 and 9.

Since 1² and 9² give 1 at unit’s place, so these are the possible values of unit digit of the square root.

2) 4 and 6

Since, 4²=16 and 6² = 36, hence, 4 and 6 are possible digits

3) 1 and 9

Since 1² and 9² give 1 at unit’s place, so these are the possible values of unit digit of the square root.

4) 5

Since, 5²= 25, hence 5 is possible.

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Hope this will help you....