Question

What is the square root of 64?

Answer 1

`sqrt64=+-8`

Answer 2

It's 8 or -8.

Explanation:

8 x 8 = 64.

Answer 3

The principal square root of `64` is:

`sqrt(64) = 8`

The other (non-principal) square root is:

`-sqrt(64) = -8`

Explanation:

`64` has two square roots, namely `8` and `-8`, since:

`8^2 = (-8)^2 = 64`

When we say "the square root", what is usually intended is "the principal square root", which in the case of the Real square root of a positive number is the positive one.

Any non-zero number `n` has two square roots. In order to distinguish between them, we call one the "principal" square root, which in the case of `n > 0` means the positive one.

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Complex footnote

If `n < 0` then it has two Complex non-Real square roots:

`+-i sqrt(-n)`

In this case we call `i sqrt(-n)` the principal square root and `-i sqrt(-n)` the non-principal one.

For example:

`sqrt(-64) = 8i` is the principal square root.

`-sqrt(-64) = -8i` is the other square root.

Note that `8i` is not "positive". Unlike Real numbers, Complex numbers are not ordered, but for pure imaginary square roots we choose the one with the positive imaginary part and call it "principal".