Algebra Examples

$\sqrt{\sqrt[3]{256}}$

Step 1

Rewrite $256$ as $4^{3} \cdot 4$ .

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Step 1.1

Factor $64$ out of $256$ .

$\sqrt{\sqrt[3]{64 (4)}}$

Step 1.2

Rewrite $64$ as $4^{3}$ .

$\sqrt{\sqrt[3]{4^{3} \cdot 4}}$

Step 2

Pull terms out from under the radical.

$\sqrt{4 \sqrt[3]{4}}$

Step 3

Rewrite $4 \sqrt[3]{4}$ as $2^{2} \sqrt[3]{2^{2}}$ .

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Step 3.1

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

$\sqrt{2^{2} \sqrt[3]{4}}$

Step 3.2

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

$\sqrt{2^{2} \sqrt[3]{2^{2}}}$

Step 4

Pull terms out from under the radical.

$2 \sqrt{\sqrt[3]{2^{2}}}$

Step 5

Raise $2$ to the power of $2$ .

$2 \sqrt{\sqrt[3]{4}}$

Step 6

Rewrite $\sqrt{\sqrt[3]{4}}$ as $\sqrt[6]{4}$ .

$2 \sqrt[6]{4}$

Step 7

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

$2 \sqrt[6]{2^{2}}$

Step 8

Rewrite $\sqrt[6]{2^{2}}$ as $\sqrt[3]{\sqrt{2^{2}}}$ .

$2 \sqrt[3]{\sqrt{2^{2}}}$

Step 9

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

$2 \sqrt[3]{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{2}$

Decimal Form:

$2.51984209 \dots$