# How do you solve (18-n)^(1/2)=(n/8)^(1/2)?

Sep 22, 2017

$n = 16$

#### Explanation:

This is much easier to solve than it first appears. Notice that both powers are the same on each side of the equality. If the powers are the same and they are equal, the the bases must also be equal. Therefore:

$\left(18 - n\right) = \left(\frac{n}{8}\right)$

So solve for $n$:

$18 - n = \frac{n}{8} \implies 144 - 8 n = n \implies 144 = 9 n \implies n = \frac{144}{9} \implies n = 16$

Check:

${\left(18 - 16\right)}^{\frac{1}{2}} = {\left(\frac{16}{8}\right)}^{\frac{1}{2}}$

${2}^{\frac{1}{2}} = {2}^{\frac{1}{2}}$