Question #f956d

2 Answers
Oct 12, 2017

No.

Explanation:

2^2=4 and 3^2 = 9 but neither 9+4=13 nor 9-4=5 is a perfect square.

Oct 12, 2017

Let's have a look.

Explanation:

Actually matters.

Let us take few cases:rarr

(1). Square of even numbers.

(2n)^2+(2n+2)^2

=5n^2+4n+4.

This is not a perfect square.

Example rarr

2^2+4^2

=4+16

=20

=4sqrt(5).

(2). Square of odd numbers.

(2n+1)^2+(2n+3)^2

=8n^2+16n+10.

This is not a perfect square.

Example rarr

1^2+3^2

=1+9

=10

(3). Square of even & odd numbers.

(2n)^2+(2n+1)^2

=8n^2+4n+1

This is not a perfect square.

Example rarr

1^2+2^2

=1+4

=5

But there are certain cases when, the third condition gets satisfied.

In certain cases, sum of squares of an even & an odd number turns to be a perfect square.

For example rarr

3^2+4^2

=9+16

=25

=5^2.

So, it does matter.

Hope it Helps:)