Solve Using the Square Root Property x^2=16/25

$x^{2} = \frac{16}{25}$

Step 1

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

$x = \pm \sqrt{\frac{16}{25}}$

Step 2

Simplify $\pm \sqrt{\frac{16}{25}}$ .

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$x = \pm \frac{\sqrt{16}}{\sqrt{25}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{4^{2}}}{\sqrt{25}}$

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

$x = \pm \frac{4}{\sqrt{25}}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{4}{\sqrt{5^{2}}}$

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

$x = \pm \frac{4}{5}$

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.

$x = \frac{4}{5}$

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

$x = - \frac{4}{5}$

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

$x = \frac{4}{5}, - \frac{4}{5}$