Basic Math Examples

$5 w^{2} \sqrt{72 w^{3}} + \sqrt{18 w^{5}}$

Step 1

Rewrite $72 w^{3}$ as ${(6 w)}^{2} \cdot (2 w)$ .

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Step 1.1

Factor $36$ out of $72$ .

$5 w^{2} \sqrt{36 (2) w^{3}} + \sqrt{18 w^{5}}$

Step 1.2

Rewrite $36$ as $6^{2}$ .

$5 w^{2} \sqrt{6^{2} \cdot 2 w^{3}} + \sqrt{18 w^{5}}$

Step 1.3

Factor out $w^{2}$ .

$5 w^{2} \sqrt{6^{2} \cdot 2 (w^{2} w)} + \sqrt{18 w^{5}}$

Step 1.4

Move $2$ .

$5 w^{2} \sqrt{6^{2} w^{2} \cdot 2 w} + \sqrt{18 w^{5}}$

Step 1.5

Rewrite $6^{2} w^{2}$ as ${(6 w)}^{2}$ .

$5 w^{2} \sqrt{{(6 w)}^{2} \cdot 2 w} + \sqrt{18 w^{5}}$

Step 1.6

Add parentheses.

$5 w^{2} \sqrt{{(6 w)}^{2} \cdot (2 w)} + \sqrt{18 w^{5}}$

Step 2

Pull terms out from under the radical.

$5 w^{2} (6 w \sqrt{2 w}) + \sqrt{18 w^{5}}$

Step 3

Multiply $w^{2}$ by $w$ by adding the exponents.

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Step 3.1

Move $w$ .

$5 (w \cdot w^{2}) (6 \sqrt{2 w}) + \sqrt{18 w^{5}}$

Step 3.2

Multiply $w$ by $w^{2}$ .

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Step 3.2.1

Raise $w$ to the power of $1$ .

$5 (w^{1} w^{2}) (6 \sqrt{2 w}) + \sqrt{18 w^{5}}$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 w^{1 + 2} (6 \sqrt{2 w}) + \sqrt{18 w^{5}}$

Step 3.3

Add $1$ and $2$ .

$5 w^{3} (6 \sqrt{2 w}) + \sqrt{18 w^{5}}$

Step 4

Multiply $6$ by $5$ .

$30 w^{3} \sqrt{2 w} + \sqrt{18 w^{5}}$

Step 5

Rewrite $18 w^{5}$ as ${(3 w^{2})}^{2} \cdot (2 w)$ .

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Step 5.1

Factor $9$ out of $18$ .

$30 w^{3} \sqrt{2 w} + \sqrt{9 (2) w^{5}}$

Step 5.2

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

$30 w^{3} \sqrt{2 w} + \sqrt{3^{2} \cdot 2 w^{5}}$

Step 5.3

Factor out $w^{4}$ .

$30 w^{3} \sqrt{2 w} + \sqrt{3^{2} \cdot 2 (w^{4} w)}$

Step 5.4

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

$30 w^{3} \sqrt{2 w} + \sqrt{3^{2} \cdot 2 ({(w^{2})}^{2} w)}$

Step 5.5

Move $2$ .

$30 w^{3} \sqrt{2 w} + \sqrt{3^{2} {(w^{2})}^{2} \cdot 2 w}$

Step 5.6

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

$30 w^{3} \sqrt{2 w} + \sqrt{{(3 w^{2})}^{2} \cdot 2 w}$

Step 5.7

Add parentheses.

$30 w^{3} \sqrt{2 w} + \sqrt{{(3 w^{2})}^{2} \cdot (2 w)}$

Step 6

Pull terms out from under the radical.

$30 w^{3} \sqrt{2 w} + 3 w^{2} \sqrt{2 w}$