Solve Using the Square Root Property h^2=9/49

$h^{2} = \frac{9}{49}$

Step 1

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

$h = \pm \sqrt{\frac{9}{49}}$

Step 2

Simplify $\pm \sqrt{\frac{9}{49}}$ .

Rewrite $\sqrt{\frac{9}{49}}$ as $\frac{\sqrt{9}}{\sqrt{49}}$ .

$h = \pm \frac{\sqrt{9}}{\sqrt{49}}$

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$h = \pm \frac{\sqrt{3^{2}}}{\sqrt{49}}$

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

$h = \pm \frac{3}{\sqrt{49}}$

Simplify the denominator.

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

$h = \pm \frac{3}{\sqrt{7^{2}}}$

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

$h = \pm \frac{3}{7}$

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.

$h = \frac{3}{7}$

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

$h = - \frac{3}{7}$

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

$h = \frac{3}{7}, - \frac{3}{7}$