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Yes. And this means that any even perfect square is always a multiple of 4 - not just 2.

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Yes.

Q: Is the square root of an even perfect square is always an even number?

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The square root of an even number can be an even number (if it is a perfect square), or an irrational number (if it is not).

No. 3 is not a perfect square, so its square root is irrational.

a perfect square; it is an even number of sides (4); and all sides are identical

Think! What if the magic square had an even number of cells. There's your answer.

One way is to get the prime factorization of the number. If every prime occurs an even number of times, it is a square, otherwise, not. Another is to estimate the square root of the number, and square it. If you get more than the number, try a lower estimate; if less, a higher one. Using interval bisection you very quickly zero in on the square root, if it is a whole number. If so, the number is a perfect square. Otherwise, you find 2 consecutive whole numbers between which is the square root, in which case it is not a perfect square.

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The square root of an even number can be an even number (if it is a perfect square), or an irrational number (if it is not).

The square of an even number is always even.

Assuming you know that your number is a perfect square, the square root of an even number is even, and the square root of an odd number is odd.

No. There's no real number you can square and get -4. Not even approximately.In fact, there's no real number you can square and get any negative number.

No. Consider 15: 1,3,5,15 Every positive whole number has an even number of factors, unless the number is a perfect square.

It is: 4

Square of any even counting number is always an even number and square of any odd number is always odd. Addition of even number and its square is always an even number because even + even results in even number and addition of odd number and its square is always an even number because odd + odd = even number. Since natural or counting numbers consists of only even and odd, which comes one by one after each other. So, according to the question and the given condition only one answer comes out which is an even number. e.g. let us take the counting number like 8, square of 8 = 82 =64 and addition of 8 and its square =8+64 =72 which is an even number.

3x3 = 9; 4x4 = 16. Those are perfect square; 12 is not the square of any integer, or even of any rational number.

Odd. I determined my answer by looking at the number of factors of a square number.

No. Perfect square numbers have an odd number of factors.

An odd number.

No. 3 is not a perfect square, so its square root is irrational.