Solve Using the Square Root Property x^2=147

$x^{2} = 147$

Step 1

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

$x = \pm \sqrt{147}$

Step 2

Simplify $\pm \sqrt{147}$ .

Rewrite $147$ as $7^{2} \cdot 3$ .

Factor $49$ out of $147$ .

$x = \pm \sqrt{49 (3)}$

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2} \cdot 3}$

Pull terms out from under the radical.

$x = \pm 7 \sqrt{3}$

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.

$x = 7 \sqrt{3}$

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

$x = - 7 \sqrt{3}$

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

$x = 7 \sqrt{3}, - 7 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 7 \sqrt{3}, - 7 \sqrt{3}$

Decimal Form:

$x = 12.12435565 \dots, - 12.12435565 \dots$