Algebra Examples

$\sqrt[3]{\sqrt{8000}}$

Step 1

Rewrite $8000$ as $40^{2} \cdot 5$ .

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Step 1.1

Factor $1600$ out of $8000$ .

$\sqrt[3]{\sqrt{1600 (5)}}$

Step 1.2

Rewrite $1600$ as $40^{2}$ .

$\sqrt[3]{\sqrt{40^{2} \cdot 5}}$

$\sqrt[3]{\sqrt{40^{2} \cdot 5}}$

Step 2

Pull terms out from under the radical.

$\sqrt[3]{40 \sqrt{5}}$

Step 3

Rewrite $40 \sqrt{5}$ as $2^{3} \cdot (5 \sqrt{5})$ .

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Step 3.1

Factor $8$ out of $40$ .

$\sqrt[3]{8 (5) \sqrt{5}}$

Step 3.2

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} \cdot 5 \sqrt{5}}$

Step 3.3

Add parentheses.

$\sqrt[3]{2^{3} \cdot (5 \sqrt{5})}$

$\sqrt[3]{2^{3} \cdot (5 \sqrt{5})}$

Step 4

Pull terms out from under the radical.

$2 \sqrt[3]{5 \sqrt{5}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{5 \sqrt{5}}$

Decimal Form:

$4.47213595 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$