Basic Math Examples

$u \sqrt{24 v^{3}} + \sqrt{\sqrt{6 v u^{2}}}$

Step 1

Rewrite $24 v^{3}$ as ${(2 v)}^{2} \cdot (6 v)$ .

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Step 1.1

Factor $4$ out of $24$ .

$u \sqrt{4 (6) v^{3}} + \sqrt{\sqrt{6 v u^{2}}}$

Step 1.2

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

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

Step 1.3

Factor out $v^{2}$ .

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

Step 1.4

Move $6$ .

$u \sqrt{2^{2} v^{2} \cdot 6 v} + \sqrt{\sqrt{6 v u^{2}}}$

Step 1.5

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

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

Step 1.6

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

$2 u v \sqrt{6 v} + \sqrt{\sqrt{6 v u^{2}}}$

Step 4

Rewrite $6 v u^{2}$ as $u^{2} \cdot (6 v)$ .

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Step 4.1

Move $v$ .

$2 u v \sqrt{6 v} + \sqrt{\sqrt{6 u^{2} v}}$

Step 4.2

Reorder $6$ and $u^{2}$ .

$2 u v \sqrt{6 v} + \sqrt{\sqrt{u^{2} \cdot 6 v}}$

Step 4.3

Add parentheses.

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

Step 5

Pull terms out from under the radical.

$2 u v \sqrt{6 v} + \sqrt{u \sqrt{6 v}}$