Precalculus Examples

$\sqrt{8^{2} + 4^{2}}$

Step 1

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

$\sqrt{64 + 4^{2}}$

Step 2

Raise $4$ to the power of $2$ .

$\sqrt{64 + 16}$

Step 3

Add $64$ and $16$ .

$\sqrt{80}$

Step 4

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 4.1

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

Step 4.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5}$

$\sqrt{4^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$4 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$