How do you simplify the radical expression sqrt72?

Mar 20, 2017

$\sqrt{72} = \sqrt{36 \times 26} = \sqrt{36} \times \sqrt{2} = 6 \times \sqrt{2}$

Explanation:

This takes advantage of the relation

$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$

Look for a factor in the original value that is a perfect square (4, 9, 16, 25, 36, etc.)

Mar 20, 2017

$6 \sqrt{2}$
$\sqrt{72}$ can also be thought of as $\sqrt{36 \cdot 2}$, or $\sqrt{6 \cdot 6 \cdot 2}$.
Using the rule that $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$, you end up with $\sqrt{6} \cdot \sqrt{6} \cdot \sqrt{2}$.
This can also be expressed as ${\sqrt{6}}^{2} \cdot \sqrt{2}$.
The square root and square cancel, leaving us with the simplified radical of $6 \sqrt{2}$.