Solve Using the Square Root Property x^2=108

$x^{2} = 108$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{108}$

Step 2

Simplify $\pm \sqrt{108}$ .

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$x = \pm \sqrt{36 (3)}$

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2} \cdot 3}$

Pull terms out from under the radical.

$x = \pm 6 \sqrt{3}$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 6 \sqrt{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 6 \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 6 \sqrt{3}, - 6 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 6 \sqrt{3}, - 6 \sqrt{3}$

Decimal Form:

$x = 10.39230484 \dots, - 10.39230484 \dots$