We are asked to solve the equation $(x-5)^2 = 18$ using the square root property. The answer should be simplified and expressed using radicals if necessary. If there are multiple solutions, they should be separated by a comma.

1. Problem Description

We are asked to solve the equation $(x-5)^2 = 18$ using the square root property. The answer should be simplified and expressed using radicals if necessary. If there are multiple solutions, they should be separated by a comma.

2. Solution Steps

To solve the equation $(x-5)^2 = 18$, we apply the square root property, which states that if $u^2 = a$, then $u = \pm \sqrt{a}$.

Applying this property to our equation, we get:

$x - 5 = \pm \sqrt{18}$

Since $18 = 9 \cdot 2$, we can simplify $\sqrt{18}$ as follows:

$\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}$

So, $x - 5 = \pm 3\sqrt{2}$.

Now, we add 5 to both sides of the equation to isolate x:

$x = 5 \pm 3\sqrt{2}$

Therefore, the two solutions are $x = 5 + 3\sqrt{2}$ and $x = 5 - 3\sqrt{2}$.

3. Final Answer

$5+3\sqrt{2}, 5-3\sqrt{2}$