Question

give reasons to show that none of the number given below is a perfect square 360
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Answer 1

$\sf{\large{\underline{\red{Question:-}}}}$

Give reasons to show that 360 is not a perfect square.

$\sf{\large{\underline{\red{Answer:-}}}}$

$\mathtt{Number:}$ 360

$\bf{\underline{\boxed{\green{Reason\:1:-}}}}$

A number that ends with an even number of zeroes is a perfect square and a number that ends with an odd number of zeroes is not a perfect square

360 ends with one(1) zeroes.

1 is odd

So 360 is not a perfect square.

$\bf{\underline{\boxed{\green{Reason\:2:-}}}}$

Break 360 into its prime factors

360 = 2 * 2 * 2 * 3 * 3 * 5

Group the prime factors in pairs

360 = (2 * 2) * 2 * (3 * 3) * 5

These 2 and 5 do not form a pair.

So 360 is not a perfect square.