# How do you simplify sqrt288?

May 23, 2015

You can factor the number inside the root:

$\sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3}$

However, $2 \cdot 2 \cdot 3 = 12$

Then, you have $\sqrt{2 \cdot 12 \cdot 12} = \sqrt{2 \cdot {12}^{2}}$.

By definition, when you have a squared number inside the square root, you can take its root out:

final answer: $12 \sqrt{2}$

May 23, 2015

In order to simplify $\sqrt{288}$ factor $288$ and look for pairs of factors

$288$
$= 2 \times 144$
$= 2 \times \textcolor{red}{12} \times \textcolor{red}{12}$
and therefore
$\sqrt{288} = \sqrt{2 \times {12}^{2}} = 12 \sqrt{2}$

If you did not recognize $144$ as ${12}^{2}$ you could have continued the factoring as
$2 \times 144$
$= 2 \times 2 \times 72$
$= 2 \times 2 \times 2 \times 36$
$= 2 \times 2 \times 2 \times 2 \times 18$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 9$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$
$= \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{b l u e}{2} \times \textcolor{b l u e}{2} \times 2 \times \textcolor{\mathmr{and} a n \ge}{3} \times \textcolor{\mathmr{and} a n \ge}{3}$
So
$\sqrt{288} = \sqrt{\textcolor{red}{{2}^{2}} \cdot \textcolor{b l u e}{{2}^{2}} \cdot 2 \cdot \textcolor{\mathmr{and} a n \ge}{{3}^{2}}}$
$= \textcolor{red}{2} \cdot \textcolor{b l u e}{2} \cdot \textcolor{\mathmr{and} a n \ge}{3} \sqrt{2}$
$= 12 \sqrt{2}$