Precalculus Examples

$\sqrt{8 z^{3}} + 10 z \sqrt{2 z}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8 z^{3}$ as ${(2 z)}^{2} \cdot (2 z)$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2) z^{3}} + 10 z \sqrt{2 z}$

Step 1.1.2

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

$\sqrt{2^{2} \cdot 2 z^{3}} + 10 z \sqrt{2 z}$

Step 1.1.3

Factor out $z^{2}$ .

$\sqrt{2^{2} \cdot 2 (z^{2} z)} + 10 z \sqrt{2 z}$

Step 1.1.4

Move $2$ .

$\sqrt{2^{2} z^{2} \cdot 2 z} + 10 z \sqrt{2 z}$

Step 1.1.5

Rewrite $2^{2} z^{2}$ as ${(2 z)}^{2}$ .

$\sqrt{{(2 z)}^{2} \cdot 2 z} + 10 z \sqrt{2 z}$

Step 1.1.6

Add parentheses.

$\sqrt{{(2 z)}^{2} \cdot (2 z)} + 10 z \sqrt{2 z}$

Step 1.2

Pull terms out from under the radical.

$2 z \sqrt{2 z} + 10 z \sqrt{2 z}$

Step 2

Add $2 z \sqrt{2 z}$ and $10 z \sqrt{2 z}$ .

$12 z \sqrt{2 z}$