Algebra Examples

$\sqrt[4]{16 w^{10}} + 2 w \sqrt[4]{w^{6}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $16 w^{10}$ as ${(2 w^{2})}^{4} w^{2}$ .

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Step 1.1.1

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

$\sqrt[4]{2^{4} w^{10}} + 2 w \sqrt[4]{w^{6}}$

Step 1.1.2

Factor out $w^{8}$ .

$\sqrt[4]{2^{4} (w^{8} w^{2})} + 2 w \sqrt[4]{w^{6}}$

Step 1.1.3

Rewrite $w^{8}$ as ${(w^{2})}^{4}$ .

$\sqrt[4]{2^{4} ({(w^{2})}^{4} w^{2})} + 2 w \sqrt[4]{w^{6}}$

Step 1.1.4

Rewrite $2^{4} {(w^{2})}^{4}$ as ${(2 w^{2})}^{4}$ .

$\sqrt[4]{{(2 w^{2})}^{4} w^{2}} + 2 w \sqrt[4]{w^{6}}$

Step 1.2

Pull terms out from under the radical.

$2 w^{2} \sqrt[4]{w^{2}} + 2 w \sqrt[4]{w^{6}}$

Step 1.3

Rewrite $\sqrt[4]{w^{2}}$ as $\sqrt{\sqrt{w^{2}}}$ .

$2 w^{2} \sqrt{\sqrt{w^{2}}} + 2 w \sqrt[4]{w^{6}}$

Step 1.4

Pull terms out from under the radical, assuming positive real numbers.

$2 w^{2} \sqrt{w} + 2 w \sqrt[4]{w^{6}}$

Step 1.5

Factor out $w^{4}$ .

$2 w^{2} \sqrt{w} + 2 w \sqrt[4]{w^{4} w^{2}}$

Step 1.6

Pull terms out from under the radical.

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

Step 1.7

Multiply $w$ by $w$ by adding the exponents.

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Step 1.7.1

Move $w$ .

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

Step 1.7.2

Multiply $w$ by $w$ .

$2 w^{2} \sqrt{w} + 2 w^{2} \sqrt[4]{w^{2}}$

Step 1.8

Rewrite $\sqrt[4]{w^{2}}$ as $\sqrt{\sqrt{w^{2}}}$ .

$2 w^{2} \sqrt{w} + 2 w^{2} \sqrt{\sqrt{w^{2}}}$

Step 1.9

Pull terms out from under the radical, assuming positive real numbers.

$2 w^{2} \sqrt{w} + 2 w^{2} \sqrt{w}$

Step 2

Add $2 w^{2} \sqrt{w}$ and $2 w^{2} \sqrt{w}$ .

$4 w^{2} \sqrt{w}$