# What is the square root of 64?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

13
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.

$\textcolor{w h i t e}{}$
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".

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

5
Nov 21, 2016

It's 8 or -8.

#### Explanation:

8 x 8 = 64.

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

5
Nov 21, 2016

$\sqrt{64} = \pm 8$

• 13 minutes ago
• 14 minutes ago
• 15 minutes ago
• 18 minutes ago
• 45 seconds ago
• A minute ago
• 4 minutes ago
• 5 minutes ago
• 8 minutes ago
• 11 minutes ago
• 13 minutes ago
• 14 minutes ago
• 15 minutes ago
• 18 minutes ago