Finite Math Examples

$\sqrt{2 x (\sqrt{8 x - \sqrt{32}})}$

Step 1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.1

Factor $16$ out of $32$ .

$\sqrt{2 x \sqrt{8 x - \sqrt{16 (2)}}}$

Step 1.2

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

$\sqrt{2 x \sqrt{8 x - \sqrt{4^{2} \cdot 2}}}$

$\sqrt{2 x \sqrt{8 x - \sqrt{4^{2} \cdot 2}}}$

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $4$ by $- 1$ .

$\sqrt{2 x \sqrt{8 x - 4 \sqrt{2}}}$

Step 4

Factor $4$ out of $8 x - 4 \sqrt{2}$ .

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Step 4.1

Factor $4$ out of $8 x$ .

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

Step 4.2

Factor $4$ out of $- 4 \sqrt{2}$ .

$\sqrt{2 x \sqrt{4 (2 x) + 4 (- \sqrt{2})}}$

Step 4.3

Factor $4$ out of $4 (2 x) + 4 (- \sqrt{2})$ .

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

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

$\sqrt{2 x \cdot 2 \sqrt{2 x - \sqrt{2}}}$

Step 7

Multiply $2$ by $2$ .

$\sqrt{4 x \sqrt{2 x - \sqrt{2}}}$

Step 8

Rewrite $4 x \sqrt{2 x - \sqrt{2}}$ as $2^{2} (x \sqrt{2 x - \sqrt{2}})$ .

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Step 8.1

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

$\sqrt{2^{2} x \sqrt{2 x - \sqrt{2}}}$

Step 8.2

Add parentheses.

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

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

Step 9

Pull terms out from under the radical.

$2 \sqrt{x \sqrt{2 x - \sqrt{2}}}$

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