# How do you simplify -3sqrt(252)?

Jul 27, 2015

=color(blue)(−18sqrt(7)

#### Explanation:

−3sqrt252

Prime factorising $252$

=−3sqrt(2*2*3*3*7)

=−3sqrt(2^2 *3^2*7)
=−3(2*3)sqrt(7)

=color(blue)(−18sqrt(7)

Jul 27, 2015

You check to see if you can write $252$ as a product of a perfect square and another number.

#### Explanation:

Since $252$ is not a perfect square itself, you can check to see if you can write it as a product of a perfect square and another number.

To do that, find the prime factors of $252$

$\left\{\begin{matrix}252 : 2 = 126 \\ 126 : 2 = 63\end{matrix}\right. \to {2}^{2}$

$\left\{\begin{matrix}63 : 3 = 21 \\ 21 : 3 = 7\end{matrix}\right. \to {3}^{2}$

$7 : 7 = 1 \to {7}^{1}$

So, you can write $252$ as

$252 = {2}^{2} \cdot {3}^{2} \cdot 7 = 4 \cdot 9 \cdot 7 = {\underbrace{36}}_{\textcolor{b l u e}{= {6}^{2}}} \cdot 7$

This means that the original expression will be equivalent to

$- 3 \cdot \sqrt{252} = - 3 \cdot \sqrt{36 \cdot 7}$

$- 3 \cdot \sqrt{36} \cdot \sqrt{7} = - 3 \cdot 6 \cdot \sqrt{7} = \textcolor{g r e e n}{- 18 \sqrt{7}}$