Solve for x x^2 = square root of 16

$x^{2} = \sqrt{16}$

Step 1

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

$x = \pm \sqrt{\sqrt{16}}$

Step 2

Simplify $\pm \sqrt{\sqrt{16}}$ .

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{\sqrt{4^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \sqrt{4}$

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$