Basic Math Examples

$6 w \sqrt{2 z w a^{2}} - a \sqrt{18 w^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $2 z w a^{2}$ as $a^{2} \cdot (2 z w)$ .

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Step 1.1.1

Move $w$ .

$6 w \sqrt{2 z a^{2} w} - a \sqrt{18 w^{3}}$

Step 1.1.2

Move $z$ .

$6 w \sqrt{2 a^{2} z w} - a \sqrt{18 w^{3}}$

Step 1.1.3

Reorder $2$ and $a^{2}$ .

$6 w \sqrt{a^{2} \cdot 2 z w} - a \sqrt{18 w^{3}}$

Step 1.1.4

Add parentheses.

$6 w \sqrt{a^{2} \cdot 2 (z w)} - a \sqrt{18 w^{3}}$

Step 1.1.5

Add parentheses.

$6 w \sqrt{a^{2} \cdot (2 z w)} - a \sqrt{18 w^{3}}$

Step 1.2

Pull terms out from under the radical.

$6 w (a \sqrt{2 z w}) - a \sqrt{18 w^{3}}$

Step 1.3

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

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Step 1.3.1

Factor $9$ out of $18$ .

$6 w (a \sqrt{2 z w}) - a \sqrt{9 (2) w^{3}}$

Step 1.3.2

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

$6 w (a \sqrt{2 z w}) - a \sqrt{3^{2} \cdot 2 w^{3}}$

Step 1.3.3

Factor out $w^{2}$ .

$6 w (a \sqrt{2 z w}) - a \sqrt{3^{2} \cdot 2 (w^{2} w)}$

Step 1.3.4

Move $2$ .

$6 w (a \sqrt{2 z w}) - a \sqrt{3^{2} w^{2} \cdot 2 w}$

Step 1.3.5

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

$6 w (a \sqrt{2 z w}) - a \sqrt{{(3 w)}^{2} \cdot 2 w}$

Step 1.3.6

Add parentheses.

$6 w (a \sqrt{2 z w}) - a \sqrt{{(3 w)}^{2} \cdot (2 w)}$

Step 1.4

Pull terms out from under the radical.

$6 w (a \sqrt{2 z w}) - a (3 w \sqrt{2 w})$

Step 1.5

Multiply $3$ by $- 1$ .

$6 w (a \sqrt{2 z w}) - 3 a w \sqrt{2 w}$

Step 2

Reorder factors in $6 w (a \sqrt{2 z w}) - 3 a w \sqrt{2 w}$ .

$6 w a \sqrt{2 z w} - 3 a w \sqrt{2 w}$