How do you solve sqrtn-3=6 and check your solution?

Jan 18, 2017

See the entire solution and verification process below:

Explanation:

Step 1) Add $\textcolor{red}{3}$ to each side of the equation to isolate the $n$ term while keeping the equation balanced:

$\sqrt{n} - 3 + \textcolor{red}{3} = 6 + \textcolor{red}{3}$

$\sqrt{n} - 0 = 9$

$\sqrt{n} = 9$

Step 2) Square each side of the equation to solve for $n$ while keeping the equation balanced:

${\left(\sqrt{n}\right)}^{2} = {9}^{2}$

$n = 81$

To check the solution we substitute $\textcolor{red}{81}$ for $\textcolor{red}{n}$, evaluate the left side of the equation and ensure it equals the right side of the equation:

$\sqrt{\textcolor{red}{n}} - 3 = 6$ becomes:

$\sqrt{\textcolor{red}{81}} - 3 = 6$

$9 - 3 = 6$

$6 = 6$