Explain why all even square numbers are multiples of four?

Question

anonymous · Answer

The square of any even number is a multiple of 4 because an even number is 2n and (2n) squared is 4 (n squared).

anonymous · Answer

what about for odd numbers??

anonymous · Answer

whats the exact question

anonymous · Answer

investigate what the corresponding answer would be for square numbers which are odd

anonymous · Answer

what lvl math is this?

anonymous · Answer

For odd numbers, one could say that an odd square must be the square of an odd number, or we could say all odd squares are congruent to 1 modulo 4...just depends on what lvl class this is.

anonymous · Answer

GSCE higher tier

anonymous · Answer

hmm...there isnt an easy answer like in the even squares case.  You arent going to find that all squares of odd numbers are divisible by some number.  However,you will find that they all leave a remainder of 1 when divided by 4.

anonymous · Answer

This can be seen because:$$(2n+1)^2=4n^2+4n+1=4(n^2+n)+1=4q+1$$where q is n^2+n.  So only way to reword the whole problem is, squares of even numbers leave a remainder of 0 which divided by 4, and squares of odd numbers leave a remainder of 1.

anonymous · Answer

one* not only.

anonymous · Answer

when* geez, i should get some sleep.

anonymous · Answer

lol

anonymous · Answer

lol

anonymous · Answer

@Mrbonez could you expand on your answer about even square roots?