Give reason to show that none of the numbers given below is a perfect square:
Question:

Give reason to show that none of the numbers given below is a perfect square:

(i) 5372

(ii) 5963

(iii) 8457

(iv) 9468

(v) 360

(vi) 64000

(viii) 2500000

Solution:

By observing the properties of square numbers, we can determine whether a given number is a square or not.

(i) 5372

A number that ends with 2 is not a perfect square.

Thus, the given number is not a perfect square.

(ii) 5963

A number that ends with 3 is not a perfect square.

Thus, the given number is not a perfect square.

(iii) 8457

A number that ends with 7 is not a perfect square.

Thus, the given number is not a perfect square.

(iv) 9468

A number ending with 8 is not a perfect square.

Thus, the given number is not a perfect square.

(v) 360

Any number ending with an odd number of zeroes is not a perfect square.

Hence, the given number is not a perfect square.

(vi) 64000

Any number ending with an odd number of zeroes is not a perfect square.

Hence, the given number is not a perfect square.

(vii) 2500000

Any number ending with an odd number of zeroes is not a perfect square.

Hence, the given number is not a perfect square.

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