Prove that if n is a perfect square, then n+2 is not a perfect square.

Solution:

Perfect squares are numbers which are obtained by squaring a whole number.

Let us proceed according to the given data in the problem.

i.e n = x²

Where n is the product of x and x which is x² .

We can prove the given statement by considering an example.

Let us consider an example

x = 9

n = 9² = 81

Here, 81 is a perfect square because it is the square of a whole number.

n + 2 = 81 + 2

= 83 is not a perfect square.

Therefore, it is proved that if n is a perfect square, then n + 2 is not a perfect square.

Prove that if n is a perfect square, then n+2 is not a perfect square.

Summary:

It is proved that if n is a perfect square, then n + 2 is not a perfect square.