Algebra Examples

$2 \sqrt{8 p^{2} q^{3} r}$

Step 1

Rewrite $8 p^{2} q^{3} r$ as ${(2 p q)}^{2} \cdot (2 q r)$ .

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Step 1.1

Factor $4$ out of $8$ .

$2 \sqrt{4 (2) p^{2} q^{3} r}$

Step 1.2

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

$2 \sqrt{2^{2} \cdot 2 p^{2} q^{3} r}$

Step 1.3

Factor out $q^{2}$ .

$2 \sqrt{2^{2} \cdot 2 p^{2} (q^{2} q) r}$

Step 1.4

Move $2$ .

$2 \sqrt{2^{2} p^{2} q^{2} \cdot 2 q r}$

Step 1.5

Rewrite $2^{2} p^{2} q^{2}$ as ${(2 p q)}^{2}$ .

$2 \sqrt{{(2 p q)}^{2} \cdot 2 q r}$

Step 1.6

Add parentheses.

$2 \sqrt{{(2 p q)}^{2} \cdot 2 (q r)}$

Step 1.7

Add parentheses.

$2 \sqrt{{(2 p q)}^{2} \cdot (2 q r)}$

Step 2

Pull terms out from under the radical.

$2 (2 p q \sqrt{2 q r})$

Step 3

Multiply $2$ by $2$ .

$4 p q \sqrt{2 q r}$