Algebra Examples

$\sqrt{2 \sqrt{8}}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{2 \sqrt{4 (2)}}$

Step 1.2

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

$\sqrt{2 \sqrt{2^{2} \cdot 2}}$

$\sqrt{2 \sqrt{2^{2} \cdot 2}}$

Step 2

Pull terms out from under the radical.

$\sqrt{2 \cdot 2 \sqrt{2}}$

Step 3

Write the expression using exponents.

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Step 3.1

Multiply $2$ by $2$ .

$\sqrt{4 \sqrt{2}}$

Step 3.2

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

$\sqrt{2^{2} \sqrt{2}}$

$\sqrt{2^{2} \sqrt{2}}$

Step 4

Pull terms out from under the radical.

$2 \sqrt{\sqrt{2}}$

Step 5

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

$2 \sqrt[4]{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[4]{2}$

Decimal Form:

$2.37841423 \dots$

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