Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

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

Remove non-negative terms from the absolute value.

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

Step 1.4

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

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Factor out $w^{4}$ .

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

Step 1.7

Pull terms out from under the radical.

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

Step 1.8

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

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

Step 1.9

Pull terms out from under the radical.

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

Step 2

Reorder factors in $2 w^{2} \sqrt{| w |} + 2 w (| w | \sqrt{| w |})$ .

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