Finite Math Examples

$x^{2 \sqrt{32 x v^{2}}} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 1

Rewrite $32 x v^{2}$ as ${(4 v)}^{2} \cdot (2 x)$ .

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Step 1.1

Factor $16$ out of $32$ .

$x^{2 \sqrt{16 (2) x v^{2}}} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 1.2

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

$x^{2 \sqrt{4^{2} \cdot 2 x v^{2}}} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 1.3

Move $x$ .

$x^{2 \sqrt{4^{2} \cdot 2 v^{2} x}} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 1.4

Move $2$ .

$x^{2 \sqrt{4^{2} v^{2} \cdot 2 x}} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 1.5

Rewrite $4^{2} v^{2}$ as ${(4 v)}^{2}$ .

$x^{2 \sqrt{{(4 v)}^{2} \cdot 2 x}} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 1.6

Add parentheses.

$x^{2 \sqrt{{(4 v)}^{2} \cdot (2 x)}} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 2

Pull terms out from under the radical.

$x^{2 (4 v \sqrt{2 x})} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 3

Multiply $4$ by $2$ .

$x^{8 (v \sqrt{2 x})} + 4 \sqrt{\sqrt{18 x^{5}}}$

Step 4

Rewrite $18 x^{5}$ as ${(3 x^{2})}^{2} \cdot (2 x)$ .

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Step 4.1

Factor $9$ out of $18$ .

$x^{8 v \sqrt{2 x}} + 4 \sqrt{\sqrt{9 (2) x^{5}}}$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$x^{8 v \sqrt{2 x}} + 4 \sqrt{\sqrt{3^{2} \cdot 2 x^{5}}}$

Step 4.3

Factor out $x^{4}$ .

$x^{8 v \sqrt{2 x}} + 4 \sqrt{\sqrt{3^{2} \cdot 2 (x^{4} x)}}$

Step 4.4

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

$x^{8 v \sqrt{2 x}} + 4 \sqrt{\sqrt{3^{2} \cdot 2 ({(x^{2})}^{2} x)}}$

Step 4.5

Move $2$ .

$x^{8 v \sqrt{2 x}} + 4 \sqrt{\sqrt{3^{2} {(x^{2})}^{2} \cdot 2 x}}$

Step 4.6

Rewrite $3^{2} {(x^{2})}^{2}$ as ${(3 x^{2})}^{2}$ .

$x^{8 v \sqrt{2 x}} + 4 \sqrt{\sqrt{{(3 x^{2})}^{2} \cdot 2 x}}$

Step 4.7

Add parentheses.

$x^{8 v \sqrt{2 x}} + 4 \sqrt{\sqrt{{(3 x^{2})}^{2} \cdot (2 x)}}$

Step 5

Pull terms out from under the radical.

$x^{8 v \sqrt{2 x}} + 4 \sqrt{3 x^{2} \sqrt{2 x}}$

Step 6

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

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Step 6.1

Reorder $3$ and $x^{2}$ .

$x^{8 v \sqrt{2 x}} + 4 \sqrt{x^{2} \cdot 3 \sqrt{2 x}}$

Step 6.2

Add parentheses.

$x^{8 v \sqrt{2 x}} + 4 \sqrt{x^{2} \cdot (3 \sqrt{2 x})}$

Step 7

Pull terms out from under the radical.

$x^{8 v \sqrt{2 x}} + 4 x \sqrt{3 \sqrt{2 x}}$