Simplify the Radical Expression 6 square root of 75mp^2q^3

$6 \sqrt{75 m p^{2} q^{3}}$

Step 1

Rewrite $75 m p^{2} q^{3}$ as ${(5 p q)}^{2} \cdot (3 m q)$ .

Factor $25$ out of $75$ .

$6 \sqrt{25 (3) m p^{2} q^{3}}$

Rewrite $25$ as $5^{2}$ .

$6 \sqrt{5^{2} \cdot 3 m p^{2} q^{3}}$

Factor out $q^{2}$ .

$6 \sqrt{5^{2} \cdot 3 m p^{2} (q^{2} q)}$

Move $m$ .

$6 \sqrt{5^{2} \cdot 3 p^{2} q^{2} m q}$

Move $3$ .

$6 \sqrt{5^{2} p^{2} q^{2} \cdot 3 m q}$

Rewrite $5^{2} p^{2} q^{2}$ as ${(5 p q)}^{2}$ .

$6 \sqrt{{(5 p q)}^{2} \cdot 3 m q}$

Add parentheses.

$6 \sqrt{{(5 p q)}^{2} \cdot 3 (m q)}$

Add parentheses.

$6 \sqrt{{(5 p q)}^{2} \cdot (3 m q)}$

Step 2

Pull terms out from under the radical.

$6 (| 5 p q | \sqrt{3 m q})$

Step 3

Remove non-negative terms from the absolute value.

$6 (5 | p q | \sqrt{3 m q})$

Step 4

Multiply $5$ by $6$ .

$30 | p q | \sqrt{3 m q}$