How do you solve sqrt(2n-88)=sqrt(n/6)?

Oct 31, 2016

The solution of the equation is $n = 48$.

Explanation:

First, you must get rid of the radicals. In this case, that is achieved by squaring both sides of the equation.

${\left(\sqrt{2 n - 88}\right)}^{2} = {\left(\sqrt{\frac{n}{6}}\right)}^{2}$

$2 n - 88 = \frac{n}{6}$

Now use inverse operations to solve for $n$.

$\left(2 n - 88\right) 6 = \left(\frac{n}{6}\right) 6$

$12 n - 528 = n$
$12 n - 12 n - 528 = n - 12 n$
$- 528 = - 11 n$
$\frac{- 528}{-} 11 = \frac{- 11 n}{-} 11$

$48 = n$

Now we must check the solution to be sure that it is not extraneous. This step absolutely cannot be skipped when solving radical equations! Remember to check a solution, we put it in place of the variable in the original equation and simplify each side of the equation to see if it makes a true statement.

$\sqrt{2 \cdot 48 - 88} = \sqrt{\frac{48}{6}}$

$\sqrt{96 - 88} = \sqrt{8}$
$\sqrt{8} = 2 \sqrt{2}$
$2 \sqrt{2} = 2 \sqrt{2}$

Since the two sides of the equation simplify to be equal, $48$ is the solution of the equation.