Basic Math Examples

$7 u \sqrt{24 w^{5}} - w^{2} \sqrt{w u}$

Step 1

Rewrite $24 w^{5}$ as ${(2 w^{2})}^{2} \cdot (6 w)$ .

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Step 1.1

Factor $4$ out of $24$ .

$7 u \sqrt{4 (6) w^{5}} - w^{2} \sqrt{w u}$

Step 1.2

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

$7 u \sqrt{2^{2} \cdot 6 w^{5}} - w^{2} \sqrt{w u}$

Step 1.3

Factor out $w^{4}$ .

$7 u \sqrt{2^{2} \cdot 6 (w^{4} w)} - w^{2} \sqrt{w u}$

Step 1.4

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

$7 u \sqrt{2^{2} \cdot 6 ({(w^{2})}^{2} w)} - w^{2} \sqrt{w u}$

Step 1.5

Move $6$ .

$7 u \sqrt{2^{2} {(w^{2})}^{2} \cdot 6 w} - w^{2} \sqrt{w u}$

Step 1.6

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

$7 u \sqrt{{(2 w^{2})}^{2} \cdot 6 w} - w^{2} \sqrt{w u}$

Step 1.7

Add parentheses.

$7 u \sqrt{{(2 w^{2})}^{2} \cdot (6 w)} - w^{2} \sqrt{w u}$

Step 2

Pull terms out from under the radical.

$7 u (2 w^{2} \sqrt{6 w}) - w^{2} \sqrt{w u}$

Step 3

Multiply $2$ by $7$ .

$14 u w^{2} \sqrt{6 w} - w^{2} \sqrt{w u}$