Solve for r 36p=pr^2

$36 p = p r^{2}$

Step 1

Rewrite the equation as $p r^{2} = 36 p$ .

$p r^{2} = 36 p$

Step 2

Divide each term in $p r^{2} = 36 p$ by $p$ and simplify.

Divide each term in $p r^{2} = 36 p$ by $p$ .

$\frac{p r^{2}}{p} = \frac{36 p}{p}$

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{p r^{2}}{p} = \frac{36 p}{p}$

Divide $r^{2}$ by $1$ .

$r^{2} = \frac{36 p}{p}$

Simplify the right side.

Cancel the common factor of $p$ .

Cancel the common factor.

$r^{2} = \frac{36 p}{p}$

Divide $36$ by $1$ .

$r^{2} = 36$

Step 3

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

$r = \pm \sqrt{36}$

Step 4

Simplify $\pm \sqrt{36}$ .

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

$r = \pm \sqrt{6^{2}}$

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

$r = \pm 6$

Step 5

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.

$r = 6$

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

$r = - 6$

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

$r = 6, - 6$