Prove that the square of any even number is always a multiple of 4.

Question

asked Oct 7, 2020 38.8k views

1 Answer

Rsteward · Answer 1 · 2020-10-12T21:34:06+0000

Answer and Explanation:

To prove : The square of any even number is always a multiple of 4.

Proof :

The even numbers is defined as number end with 0,2,4,6,8 or the even number are multiple of 2.

Let the general even number be '2n'.

Squaring the number
(2n)^2=2^2* n^2

(2n)^2=4n^2

As 4 is the multiple of n².

So, If we square any even number it is always a multiple of 4.

For example,

$2^2=4=4* 1\\4^2=16=4* 4\\6^2=36=4* 9\\8^2=64=4* 16$

Hence proved.