Simplify - square root of 60m^7

$- \sqrt{60 m^{7}}$

Step 1

Rewrite $60 m^{7}$ as ${(2 m^{3})}^{2} \cdot (15 m)$ .

Factor $4$ out of $60$ .

$- \sqrt{4 (15) m^{7}}$

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

$- \sqrt{2^{2} \cdot 15 m^{7}}$

Factor out $m^{6}$ .

$- \sqrt{2^{2} \cdot 15 (m^{6} m)}$

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

$- \sqrt{2^{2} \cdot 15 ({(m^{3})}^{2} m)}$

Move $15$ .

$- \sqrt{2^{2} {(m^{3})}^{2} \cdot 15 m}$

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

$- \sqrt{{(2 m^{3})}^{2} \cdot 15 m}$

Add parentheses.

$- \sqrt{{(2 m^{3})}^{2} \cdot (15 m)}$

Step 2

Pull terms out from under the radical.

$- (2 m^{3} \sqrt{15 m})$

Step 3

Multiply $2$ by $- 1$ .

$- 2 m^{3} \sqrt{15 m}$