Precalculus Examples

$\sqrt[4]{32 x} + \sqrt[4]{2 x^{5}}$

Step 1

Rewrite $32 x$ as $2^{4} \cdot (2 x)$ .

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Step 1.1

Factor $16$ out of $32$ .

$\sqrt[4]{16 (2) x} + \sqrt[4]{2 x^{5}}$

Step 1.2

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

$\sqrt[4]{2^{4} \cdot 2 x} + \sqrt[4]{2 x^{5}}$

Step 1.3

Add parentheses.

$\sqrt[4]{2^{4} \cdot (2 x)} + \sqrt[4]{2 x^{5}}$

$\sqrt[4]{2^{4} \cdot (2 x)} + \sqrt[4]{2 x^{5}}$

Step 2

Pull terms out from under the radical.

$2 \sqrt[4]{2 x} + \sqrt[4]{2 x^{5}}$

Step 3

Rewrite $2 x^{5}$ as $x^{4} \cdot (2 x)$ .

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Step 3.1

Factor out $x^{4}$ .

$2 \sqrt[4]{2 x} + \sqrt[4]{2 (x^{4} x)}$

Step 3.2

Reorder $2$ and $x^{4}$ .

$2 \sqrt[4]{2 x} + \sqrt[4]{x^{4} \cdot 2 x}$

Step 3.3

Add parentheses.

$2 \sqrt[4]{2 x} + \sqrt[4]{x^{4} \cdot (2 x)}$

$2 \sqrt[4]{2 x} + \sqrt[4]{x^{4} \cdot (2 x)}$

Step 4

Pull terms out from under the radical.

$2 \sqrt[4]{2 x} + x \sqrt[4]{2 x}$

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