# How do you solve \sqrt { 7u + 6} = \sqrt { 5u + 16}?

Mar 13, 2017

$u = 5$

#### Explanation:

$\sqrt{7 u + 6} = \sqrt{5 u + 16}$

square both sides

${\left(\sqrt{7 u + 6}\right)}^{2} = {\left(\sqrt{5 u + 16}\right)}^{2}$

$7 u + 6 = 5 u + 16$

move $5 u$ to left hand side and $6$ to right hand side

$7 u - 5 u = 16 - 6$

$2 u = 10$

divide both sides with $2$

$\frac{2 u}{2} = \frac{10}{2}$

$u = 5$

Mar 13, 2017

$u = 5$

#### Explanation:

color(blue)(sqrt(7u+6)=sqrt(5u+16)

To find the value of $u$, we need to isolate it. We should balance both sides (applying same operations)

Square both sides to remove the radical signs

$\rightarrow {\left(\sqrt{7 u + 6}\right)}^{\textcolor{red}{2}} = {\left(\sqrt{5 u + 16}\right)}^{\textcolor{red}{2}}$

$\rightarrow 7 u + 6 = 5 u + 16$

Subtract $6$ both sides

$\rightarrow 7 u + 6 - \textcolor{red}{6} = 5 u + 16 - \textcolor{red}{6}$

$\rightarrow 7 u = 5 u + 10$

Subtract $5 u$ both sides

$\rightarrow 7 u - \textcolor{red}{5 u} = 5 u + 10 - \textcolor{red}{5}$

$\rightarrow 2 u = 10$

Divide both sides by $2$

$\rightarrow \frac{\cancel{2} u}{\textcolor{red}{\cancel{2}}} = \frac{10}{\textcolor{red}{2}}$

color(green)(rArru=5

Hope this helps! :)