Trigonometry Examples

$\sqrt{8 \cdot \sqrt{8}}$

Step 1

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

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{8 \sqrt{4 (2)}}$

Step 1.2

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

$\sqrt{8 \sqrt{2^{2} \cdot 2}}$

$\sqrt{8 \sqrt{2^{2} \cdot 2}}$

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $8$ by $2$ .

$\sqrt{16 \sqrt{2}}$

Step 4

Rewrite $16 \sqrt{2}$ as ${(2^{2})}^{2} \sqrt{2}$ .

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Step 4.1

Rewrite $16$ as $4^{2}$ .

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

Step 4.2

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

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

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

Step 7

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

$4 \sqrt[4]{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt[4]{2}$

Decimal Form:

$4.75682846 \dots$

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