Solve for c 8^2+15^2=c^2

$8^{2} + 15^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 8^{2} + 15^{2}$ .

$c^{2} = 8^{2} + 15^{2}$

Step 2

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

$c = \pm \sqrt{8^{2} + 15^{2}}$

Step 3

Simplify $\pm \sqrt{8^{2} + 15^{2}}$ .

Raise $8$ to the power of $2$ .

$c = \pm \sqrt{64 + 15^{2}}$

Raise $15$ to the power of $2$ .

$c = \pm \sqrt{64 + 225}$

Add $64$ and $225$ .

$c = \pm \sqrt{289}$

Rewrite $289$ as $17^{2}$ .

$c = \pm \sqrt{17^{2}}$

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

$c = \pm 17$

Step 4

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.

$c = 17$

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

$c = - 17$

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

$c = 17, - 17$