Algebra Examples

$\sqrt{\sqrt[3]{4^{10}}}$

Step 1

Raise $4$ to the power of $10$ .

$\sqrt{\sqrt[3]{1048576}}$

Step 2

Rewrite $1048576$ as $64^{3} \cdot 4$ .

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Step 2.1

Factor $262144$ out of $1048576$ .

$\sqrt{\sqrt[3]{262144 (4)}}$

Step 2.2

Rewrite $262144$ as $64^{3}$ .

$\sqrt{\sqrt[3]{64^{3} \cdot 4}}$

Step 3

Pull terms out from under the radical.

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

Step 4

Rewrite $64 \sqrt[3]{4}$ as $8^{2} \sqrt[3]{2^{2}}$ .

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Step 4.1

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} \sqrt[3]{4}}$

Step 4.2

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

$\sqrt{8^{2} \sqrt[3]{2^{2}}}$

Step 5

Pull terms out from under the radical.

$8 \sqrt{\sqrt[3]{2^{2}}}$

Step 6

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

$8 \sqrt{\sqrt[3]{4}}$

Step 7

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

$8 \sqrt[6]{4}$

Step 8

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

$8 \sqrt[6]{2^{2}}$

Step 9

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

$8 \sqrt[3]{\sqrt{2^{2}}}$

Step 10

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

$8 \sqrt[3]{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt[3]{2}$

Decimal Form:

$10.07936839 \dots$