# What is the square root of 108 in simplest radical form?

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Pluma Share
Jun 30, 2016

$6 \sqrt{3}$

#### Explanation:

By factoring, we get

$\sqrt{108}$ $= \sqrt{36 \cdot 3}$

$36 = {6}^{2}$ so it is a perfect square.
We can take it out of the radical sign.

$\sqrt{108}$ = $6 \sqrt{3}$

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Dec 20, 2016

$\sqrt{108} = \textcolor{b l u e}{6 \sqrt{3}}$

#### Explanation:

Decomposing $108$ into factors one step at a time:
$108$
$\textcolor{w h i t e}{\text{XXX}} = 2 \times 54$
$\textcolor{w h i t e}{\text{XXX}} = 2 \times 2 \times 27$
$\textcolor{w h i t e}{\text{XXX}} = 2 \times 2 \times 3 \times 9$
$\textcolor{w h i t e}{\text{XXX}} = 2 \times 2 \times 3 \times 3 \times 3$
$\textcolor{w h i t e}{\text{XXX}} = {2}^{2} \times {3}^{2} \times 3$

$\sqrt{108} = \sqrt{{2}^{2} \times {3}^{2} \times 3}$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{2}^{2}} \times \sqrt{{3}^{2}} \times \sqrt{3}$
$\textcolor{w h i t e}{\text{XXX}} = 2 \times 3 \times \sqrt{3}$
$\textcolor{w h i t e}{\text{XXX}} = 6 \sqrt{3}$

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