Algebra Examples

$\sqrt[4]{36 w^{6}}$

Step 1

Rewrite $36 w^{6}$ as $w^{4} \cdot (36 w^{2})$ .

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Step 1.1

Factor out $w^{4}$ .

$\sqrt[4]{36 (w^{4} w^{2})}$

Step 1.2

Reorder $36$ and $w^{4}$ .

$\sqrt[4]{w^{4} \cdot 36 w^{2}}$

Step 1.3

Add parentheses.

$\sqrt[4]{w^{4} \cdot (36 w^{2})}$

Step 2

Pull terms out from under the radical.

$| w | \sqrt[4]{36 w^{2}}$

Step 3

Rewrite $36 w^{2}$ as ${(6 w)}^{2}$ .

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

Step 4

Rewrite $\sqrt[4]{{(6 w)}^{2}}$ as $\sqrt{\sqrt{{(6 w)}^{2}}}$ .

$| w | \sqrt{\sqrt{{(6 w)}^{2}}}$

Step 5

Pull terms out from under the radical.

$| w | \sqrt{| 6 w |}$

Step 6

Remove non-negative terms from the absolute value.

$| w | \sqrt{6 | w |}$