# How do you simplify (5 + 2sqrt7)^2?

Aug 8, 2017

See a solution process below:

#### Explanation:

We can use this rule to simplify the expression:

${\left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right)}^{2} = {\textcolor{red}{x}}^{2} + 2 \textcolor{red}{x} \textcolor{b l u e}{y} + {\textcolor{b l u e}{y}}^{2}$

Substituting $\textcolor{red}{5}$ for $\textcolor{red}{x}$ and substituting $\textcolor{red}{2 \sqrt{7}}$ for $\textcolor{b l u e}{y}$ gives:

${\left(\textcolor{red}{5} + \textcolor{b l u e}{y}\right)}^{2} \implies {\textcolor{red}{5}}^{2} + \left(2 \cdot \textcolor{red}{5} \cdot \textcolor{b l u e}{2 \sqrt{7}}\right) + {\textcolor{b l u e}{\left(2 \sqrt{7}\right)}}^{2} \implies$

$25 + 20 \sqrt{7} + \left(4 \cdot 7\right) \implies$

$25 + 20 \sqrt{7} + 28 \implies$

$25 + 28 + 20 \sqrt{7} \implies$

$53 + 20 \sqrt{7}$