# How do you solve (p + 7) ^ { 2} = 216?

Dec 7, 2017

$p = - 7 \pm 6 \sqrt{6}$

#### Explanation:

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\sqrt{{\left(p + 7\right)}^{2}} = \pm \sqrt{216} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\Rightarrow p + 7 = \pm 6 \sqrt{6}$

$\text{subtract 7 from both sides}$

$p \cancel{+ 7} \cancel{- 7} = - 7 \pm 6 \sqrt{6}$

$\Rightarrow p = - 7 \pm 6 \sqrt{6} \leftarrow \textcolor{red}{\text{exact solutions}}$

Dec 7, 2017

$p = - 7 \pm 6 \sqrt{6}$

#### Explanation:

${\left(p + 7\right)}^{2} = 216$

$\rightarrow p + 7 = \pm \sqrt{216}$

$\textcolor{w h i t e}{\text{XXX}} 226 = {2}^{2} \cdot {3}^{2} \cdot 6 = {6}^{2} \cdot 6$

$\rightarrow p + 7 = \pm 6 \sqrt{6}$

$\rightarrow p = - 7 \pm \sqrt{6}$

Dec 7, 2017

$p \approx 7.70$

#### Explanation:

Alright, so we need to isolate the $p$ on one side of the equation so that we can solve this.

To do that, we are going to start with taking the square root of both sides.

$\sqrt{{\left(p + 7\right)}^{2}} = \pm \sqrt{216}$

The square root and the square will cancel out so all we have to do is finish the equation!

$p + 7 \approx 14.70$
$p + 7 - 7 \approx 14.70 - 7$
$p \approx 7.70$

Also, I would like to add that is not the exact number, IT IS AN APPROXIMATION. If you would like to have the exact number, see below. Since $\sqrt{216}$ can not be completely squared, it would have to be reduced to

$p + 7 = \pm \sqrt{216}$
$p + 7 = \pm 6 \sqrt{6}$
$p = - 7 \pm 6 \sqrt{6}$

Hope that helps!
~Chandler Dowd