Finite Math Examples

$\sqrt{6 \cdot \sqrt{216}}$

Step 1

Rewrite $216$ as $6^{2} \cdot 6$ .

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Step 1.1

Factor $36$ out of $216$ .

$\sqrt{6 \sqrt{36 (6)}}$

Step 1.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6 \sqrt{6^{2} \cdot 6}}$

$\sqrt{6 \sqrt{6^{2} \cdot 6}}$

Step 2

Pull terms out from under the radical.

$\sqrt{6 \cdot 6 \sqrt{6}}$

Step 3

Write the expression using exponents.

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Step 3.1

Multiply $6$ by $6$ .

$\sqrt{36 \sqrt{6}}$

Step 3.2

Rewrite $36$ as $6^{2}$ .

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

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

Step 4

Pull terms out from under the radical.

$6 \sqrt{\sqrt{6}}$

Step 5

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

$6 \sqrt[4]{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt[4]{6}$

Decimal Form:

$9.39050748 \dots$

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