# How do you solve sqrt(4n^2) = 1/3?

Oct 7, 2015

$n = \frac{1}{6}$

#### Explanation:

Square both sides: $4 {n}^{2} = \frac{1}{9}$

Divide throughout by 4: ${n}^{2} = \frac{1}{36}$

Square root both sides: $n = \pm \sqrt{\frac{1}{36}}$

Solution: $n = \pm \frac{1}{6}$

Comment: $\left(- n\right) \left(- n\right) = \left(+ n\right) \left(+ n\right) = {n}^{2}$ so you have to have both a positive and negative solution.