# How do you solve and check for extraneous solutions in sqrt(4n) =2?

Aug 1, 2015

$\textcolor{red}{n = 1}$ is a solution.
There are $\textcolor{red}{\text{no}}$ extraneous solutions.

#### Explanation:

SOLVE:

$\sqrt{4 n} = 2$

Square each side.

$4 n = 4$

Divide each side by 4.

$n = 1$

CHECK FOR EXTRANEOUS SOLUTIONS

$\sqrt{4 n} = 2$

If $n = 1$,

$\sqrt{4 \left(1\right)} = 2$

$\sqrt{4} = 2$

$2 = 2$

$n = 1$ is a solution.

There are no extraneous solutions.