Simplify the Radical Expression square root of 200m^4n

$\sqrt{200 m^{4}} n$

Step 1

Rewrite $200 m^{4}$ as ${(10 m^{2})}^{2} \cdot 2$ .

Factor $100$ out of $200$ .

$\sqrt{100 (2) m^{4}} n$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 2 m^{4}} n$

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

$\sqrt{10^{2} \cdot 2 {(m^{2})}^{2}} n$

Move $2$ .

$\sqrt{10^{2} {(m^{2})}^{2} \cdot 2} n$

Rewrite $10^{2} {(m^{2})}^{2}$ as ${(10 m^{2})}^{2}$ .

$\sqrt{{(10 m^{2})}^{2} \cdot 2} n$

Step 2

Pull terms out from under the radical.

$| 10 m^{2} | \sqrt{2} n$

Step 3

Remove non-negative terms from the absolute value.

$10 m^{2} \sqrt{2} n$