Simplify 3v square root of 4q^7r^12y^5

$3 v \sqrt{4 q^{7} r^{12} y^{5}}$

Step 1

Rewrite $4 q^{7} r^{12} y^{5}$ as ${(2 q^{3} r^{6} y^{2})}^{2} (q y)$ .

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

$3 v \sqrt{2^{2} q^{7} r^{12} y^{5}}$

Factor out $q^{6}$ .

$3 v \sqrt{2^{2} (q^{6} q) r^{12} y^{5}}$

Rewrite $q^{6}$ as ${(q^{3})}^{2}$ .

$3 v \sqrt{2^{2} ({(q^{3})}^{2} q) r^{12} y^{5}}$

Rewrite $r^{12}$ as ${(r^{6})}^{2}$ .

$3 v \sqrt{2^{2} ({(q^{3})}^{2} q) {(r^{6})}^{2} y^{5}}$

Factor out $y^{4}$ .

$3 v \sqrt{2^{2} ({(q^{3})}^{2} q) {(r^{6})}^{2} (y^{4} y)}$

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

$3 v \sqrt{2^{2} ({(q^{3})}^{2} q) {(r^{6})}^{2} ({(y^{2})}^{2} y)}$

Move $q$ .

$3 v \sqrt{2^{2} ({(q^{3})}^{2}) {(r^{6})}^{2} {(y^{2})}^{2} q y}$

Rewrite $2^{2} ({(q^{3})}^{2}) {(r^{6})}^{2} {(y^{2})}^{2}$ as ${(2 q^{3} r^{6} y^{2})}^{2}$ .

$3 v \sqrt{{(2 q^{3} r^{6} y^{2})}^{2} q y}$

Add parentheses.

$3 v \sqrt{{(2 q^{3} r^{6} y^{2})}^{2} (q y)}$

Step 2

Pull terms out from under the radical.

$3 v (2 q^{3} r^{6} y^{2} \sqrt{q y})$

Step 3

Multiply $2$ by $3$ .

$6 v q^{3} r^{6} y^{2} \sqrt{q y}$