Evaluate x^2=36/49

$x^{2} = \frac{36}{49}$

Step 1

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

$x = \pm \sqrt{\frac{36}{49}}$

Step 2

Simplify $\pm \sqrt{\frac{36}{49}}$ .

Rewrite $\sqrt{\frac{36}{49}}$ as $\frac{\sqrt{36}}{\sqrt{49}}$ .

$x = \pm \frac{\sqrt{36}}{\sqrt{49}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{6^{2}}}{\sqrt{49}}$

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

$x = \pm \frac{6}{\sqrt{49}}$

Simplify the denominator.

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

$x = \pm \frac{6}{\sqrt{7^{2}}}$

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

$x = \pm \frac{6}{7}$

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.

$x = \frac{6}{7}$

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

$x = - \frac{6}{7}$

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

$x = \frac{6}{7}, - \frac{6}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{7}, - \frac{6}{7}$

Decimal Form:

$x = 0.\overline{857142}, - 0.\overline{857142}$