Pre-Algebra Examples

$3 u \sqrt{8 v^{5}} - v^{2} \sqrt{18 v u^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8 v^{5}$ as ${(2 v^{2})}^{2} \cdot (2 v)$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$3 u \sqrt{4 (2) v^{5}} - v^{2} \sqrt{18 v u^{2}}$

Step 1.1.2

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

$3 u \sqrt{2^{2} \cdot 2 v^{5}} - v^{2} \sqrt{18 v u^{2}}$

Step 1.1.3

Factor out $v^{4}$ .

$3 u \sqrt{2^{2} \cdot 2 (v^{4} v)} - v^{2} \sqrt{18 v u^{2}}$

Step 1.1.4

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

$3 u \sqrt{2^{2} \cdot 2 ({(v^{2})}^{2} v)} - v^{2} \sqrt{18 v u^{2}}$

Step 1.1.5

Move $2$ .

$3 u \sqrt{2^{2} {(v^{2})}^{2} \cdot 2 v} - v^{2} \sqrt{18 v u^{2}}$

Step 1.1.6

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

$3 u \sqrt{{(2 v^{2})}^{2} \cdot 2 v} - v^{2} \sqrt{18 v u^{2}}$

Step 1.1.7

Add parentheses.

$3 u \sqrt{{(2 v^{2})}^{2} \cdot (2 v)} - v^{2} \sqrt{18 v u^{2}}$

Step 1.2

Pull terms out from under the radical.

$3 u (2 v^{2} \sqrt{2 v}) - v^{2} \sqrt{18 v u^{2}}$

Step 1.3

Multiply $2$ by $3$ .

$6 u (v^{2} \sqrt{2 v}) - v^{2} \sqrt{18 v u^{2}}$

Step 1.4

Rewrite $18 v u^{2}$ as ${(3 u)}^{2} \cdot (2 v)$ .

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Step 1.4.1

Factor $9$ out of $18$ .

$6 u v^{2} \sqrt{2 v} - v^{2} \sqrt{9 (2) v u^{2}}$

Step 1.4.2

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

$6 u v^{2} \sqrt{2 v} - v^{2} \sqrt{3^{2} \cdot 2 v u^{2}}$

Step 1.4.3

Move $v$ .

$6 u v^{2} \sqrt{2 v} - v^{2} \sqrt{3^{2} \cdot 2 u^{2} v}$

Step 1.4.4

Move $2$ .

$6 u v^{2} \sqrt{2 v} - v^{2} \sqrt{3^{2} u^{2} \cdot 2 v}$

Step 1.4.5

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

$6 u v^{2} \sqrt{2 v} - v^{2} \sqrt{{(3 u)}^{2} \cdot 2 v}$

Step 1.4.6

Add parentheses.

$6 u v^{2} \sqrt{2 v} - v^{2} \sqrt{{(3 u)}^{2} \cdot (2 v)}$

Step 1.5

Pull terms out from under the radical.

$6 u v^{2} \sqrt{2 v} - v^{2} (3 u \sqrt{2 v})$

Step 1.6

Multiply $3$ by $- 1$ .

$6 u v^{2} \sqrt{2 v} - 3 v^{2} (u \sqrt{2 v})$

Step 2

Subtract $3 v^{2} (u \sqrt{2 v})$ from $6 u v^{2} \sqrt{2 v}$ .

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Step 2.1

Move $v^{2}$ .

$6 u v^{2} \sqrt{2 v} - 3 u v^{2} \sqrt{2 v}$

Step 2.2

Subtract $3 u v^{2} \sqrt{2 v}$ from $6 u v^{2} \sqrt{2 v}$ .

$3 u v^{2} \sqrt{2 v}$