Simplify square root of 75qr^3

$\sqrt{75 q r^{3}}$

Step 1

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

Factor $25$ out of $75$ .

$\sqrt{25 (3) q r^{3}}$

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

$\sqrt{5^{2} \cdot 3 q r^{3}}$

Factor out $r^{2}$ .

$\sqrt{5^{2} \cdot 3 q (r^{2} r)}$

Move $q$ .

$\sqrt{5^{2} \cdot 3 r^{2} q r}$

Move $3$ .

$\sqrt{5^{2} r^{2} \cdot 3 q r}$

Rewrite $5^{2} r^{2}$ as ${(5 r)}^{2}$ .

$\sqrt{{(5 r)}^{2} \cdot 3 q r}$

Add parentheses.

$\sqrt{{(5 r)}^{2} \cdot 3 (q r)}$

Add parentheses.

$\sqrt{{(5 r)}^{2} \cdot (3 q r)}$

Step 2

Pull terms out from under the radical.

$5 r \sqrt{3 q r}$