Trigonometry Examples

$\frac{4 \sqrt{2 z}}{\sqrt{z^{3}}}$

Step 1

Combine $\sqrt{2 z}$ and $\sqrt{z^{3}}$ into a single radical.

$4 \sqrt{\frac{2 z}{z^{3}}}$

Step 2

Reduce the expression $\frac{2 z}{z^{3}}$ by cancelling the common factors.

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Step 2.1

Factor $z$ out of $2 z$ .

$4 \sqrt{\frac{z \cdot 2}{z^{3}}}$

Step 2.2

Factor $z$ out of $z^{3}$ .

$4 \sqrt{\frac{z \cdot 2}{z \cdot z^{2}}}$

Step 2.3

Cancel the common factor.

$4 \sqrt{\frac{z \cdot 2}{z \cdot z^{2}}}$

Step 2.4

Rewrite the expression.

$4 \sqrt{\frac{2}{z^{2}}}$

Step 3

Rewrite $\frac{2}{z^{2}}$ as ${(\frac{1}{z})}^{2} \cdot 2$ .

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Step 3.1

Factor the perfect power $1^{2}$ out of $2$ .

$4 \sqrt{\frac{1^{2} \cdot 2}{z^{2}}}$

Step 3.2

Factor the perfect power $z^{2}$ out of $z^{2}$ .

$4 \sqrt{\frac{1^{2} \cdot 2}{z^{2} \cdot 1}}$

Step 3.3

Rearrange the fraction $\frac{1^{2} \cdot 2}{z^{2} \cdot 1}$ .

$4 \sqrt{{(\frac{1}{z})}^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$4 (\frac{1}{z} \sqrt{2})$

Step 5

Combine $\frac{1}{z}$ and $\sqrt{2}$ .

$4 \frac{\sqrt{2}}{z}$

Step 6

Combine $4$ and $\frac{\sqrt{2}}{z}$ .

$\frac{4 \sqrt{2}}{z}$