# How do you solve sqrt(n-5)=2sqrt3 and check your solution?

Nov 6, 2017

$n = 17$

#### Explanation:

If you square both sides you will get rid of the square roots and from there it is plain sailing.

${\sqrt{n - 5}}^{2} = {\left(2 \sqrt{3}\right)}^{2}$

$n - 5 = 4 \times 3$

$n - 5 = 12$

$n = 12 + 5 = 17$

To check the solution, substitute the value for $n$ into the original equation.

Is $\sqrt{n - 5} = 2 \sqrt{3}$?

$\sqrt{17 - 5}$

$= \sqrt{12}$

$= \sqrt{4 \times 3}$

$= 2 \sqrt{3} \text{ }$ this checks out and the solution is correct.