# What is the square root of 64?

Nov 21, 2016

$\sqrt{64} = \pm 8$

Nov 21, 2016

It's 8 or -8.

#### Explanation:

8 x 8 = 64.

Nov 21, 2016

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:

${8}^{2} = {\left(- 8\right)}^{2} = 64$

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:

$\pm i \sqrt{- n}$

In this case we call $i \sqrt{- n}$ the principal square root and $- i \sqrt{- n}$ the non-principal one.

For example:

$\sqrt{- 64} = 8 i$ is the principal square root.

$- \sqrt{- 64} = - 8 i$ is the other square root.

Note that $8 i$ 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".