# How do you simplify sqrt(72)?

Jul 1, 2015

$\sqrt{72} = 6 \sqrt{2}$

#### Explanation:

Check to see if $72$ is divisible by a perfect square:
${2}^{2} = 4$ and $72 = 4 \cdot 18$
So $\sqrt{72} = \sqrt{4 \cdot 18} = \sqrt{4} \cdot \sqrt{18} = 2 \sqrt{18}$

Continue be checking to see is $18$ is divisible by a perfect square:
${2}^{2} = 4$, and $18$ is not divisible by $4$
${3}^{2} = 9$ and $18 = 9 \cdot 2$

so we get:
$\sqrt{72} = 2 \sqrt{18} = 2 \sqrt{9 \cdot 2} = 2 \sqrt{9} \sqrt{2} = 2 \cdot 3 \sqrt{3} = 6 \sqrt{2}$

There are many ways of writing/working this simplification. Here are a few more:

$\sqrt{72} = \sqrt{4 \cdot 9 \cdot 2} = 2 \cdot 3 \cdot \sqrt{2} = 6 \sqrt{2}$

$\sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \sqrt{2} = 6 \sqrt{2}$

$\sqrt{72} = \sqrt{{2}^{3} \cdot {3}^{2}} = \sqrt{{2}^{2} \cdot 2 \cdot {3}^{2}} = 2 \cdot \sqrt{2} \cdot 3 = 6 \sqrt{2}$