Basic Math Examples

$u \sqrt{24 u v^{2}} + \sqrt{\sqrt{54 u^{3}}}$

Step 1

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

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Step 1.1

Factor $4$ out of $24$ .

$u \sqrt{4 (6) u v^{2}} + \sqrt{\sqrt{54 u^{3}}}$

Step 1.2

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

$u \sqrt{2^{2} \cdot 6 u v^{2}} + \sqrt{\sqrt{54 u^{3}}}$

Step 1.3

Move $u$ .

$u \sqrt{2^{2} \cdot 6 v^{2} u} + \sqrt{\sqrt{54 u^{3}}}$

Step 1.4

Move $6$ .

$u \sqrt{2^{2} v^{2} \cdot 6 u} + \sqrt{\sqrt{54 u^{3}}}$

Step 1.5

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

$u \sqrt{{(2 v)}^{2} \cdot 6 u} + \sqrt{\sqrt{54 u^{3}}}$

Step 1.6

Add parentheses.

$u \sqrt{{(2 v)}^{2} \cdot (6 u)} + \sqrt{\sqrt{54 u^{3}}}$

Step 2

Pull terms out from under the radical.

$u (2 v \sqrt{6 u}) + \sqrt{\sqrt{54 u^{3}}}$

Step 3

Rewrite using the commutative property of multiplication.

$2 u (v \sqrt{6 u}) + \sqrt{\sqrt{54 u^{3}}}$

Step 4

Rewrite $54 u^{3}$ as ${(3 u)}^{2} \cdot (6 u)$ .

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Step 4.1

Factor $9$ out of $54$ .

$2 u (v \sqrt{6 u}) + \sqrt{\sqrt{9 (6) u^{3}}}$

Step 4.2

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

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

Step 4.3

Factor out $u^{2}$ .

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

Step 4.4

Move $6$ .

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

Step 4.5

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

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

Step 4.6

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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