Q. 24.1( 156 Votes )

The following numbers are obviously not perfect squares. Give reason

(i) 1057 (ii) 23453

(iii) 7928 (iv) 222222

(v) 64000 (vi) 89722

(vii) 222000 (viii) 505050

Answer :

Squares of any number have :  0, 1, 4, 5, 6, 9 as the unit digit. If there is a number with its unit's digit other than 1, 4, 5, 6, 9 and 0 then the number is not a square root.

And also note that the number of zeroes in the number should also be even for being a square root.


(i) 1057 has its unit place digit as 7

Hence, it cannot be a perfect square


(ii) 23453 has its unit place digit as 3


Hence, it cannot be a perfect square


(iii) 7928 has its unit place digit as 8


Hence, it cannot be a perfect square


(iv) 222222 has its unit place digit as 2


Hence, it cannot be a perfect square


(v) 64000 has three zeros at the end of it. However, since a perfect square cannot end with odd number of zeroes, it is not a perfect square


(vi) 89722 has its unit place digit as 2


Hence, it cannot be a perfect square


(vii) 222000 has three zeroes at the end of it. And, we know that a perfect square cannot end with odd number of zeroes.


Hence, it is not a perfect square


(viii) 505050 has one zero at the end of it.


And we know that, a perfect square cannot end with odd number of zeroes,


Therefore, it is not a perfect square

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