Precalculus Examples

$5^{2} + 8^{2} = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 5^{2} + 8^{2}$ .

$c^{2} = 5^{2} + 8^{2}$

Step 2

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

$c = \pm \sqrt{5^{2} + 8^{2}}$

Step 3

Simplify $\pm \sqrt{5^{2} + 8^{2}}$ .

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Step 3.1

Raise $5$ to the power of $2$ .

$c = \pm \sqrt{25 + 8^{2}}$

Step 3.2

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

$c = \pm \sqrt{25 + 64}$

Step 3.3

Add $25$ and $64$ .

$c = \pm \sqrt{89}$

Step 4

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

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$c = \sqrt{89}$

Step 4.2

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

$c = - \sqrt{89}$

Step 4.3

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

$c = \sqrt{89}, - \sqrt{89}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = \sqrt{89}, - \sqrt{89}$

Decimal Form:

$c = 9.43398113 \dots, - 9.43398113 \dots$