Simplify the Radical Expression 7 square root of 192m^9n^2

$7 \sqrt{192 m^{9} n^{2}}$

Step 1

Rewrite $192 m^{9} n^{2}$ as ${(8 m^{4} n)}^{2} \cdot (3 m)$ .

Factor $64$ out of $192$ .

$7 \sqrt{64 (3) m^{9} n^{2}}$

Rewrite $64$ as $8^{2}$ .

$7 \sqrt{8^{2} \cdot 3 m^{9} n^{2}}$

Factor out $m^{8}$ .

$7 \sqrt{8^{2} \cdot 3 (m^{8} m) n^{2}}$

Rewrite $m^{8}$ as ${(m^{4})}^{2}$ .

$7 \sqrt{8^{2} \cdot 3 ({(m^{4})}^{2} m) n^{2}}$

Move $m$ .

$7 \sqrt{8^{2} \cdot 3 ({(m^{4})}^{2}) n^{2} m}$

Move $3$ .

$7 \sqrt{(8^{2} ({(m^{4})}^{2})) n^{2} \cdot 3 m}$

Rewrite $(8^{2} ({(m^{4})}^{2})) n^{2}$ as ${(8 m^{4} n)}^{2}$ .

$7 \sqrt{{(8 m^{4} n)}^{2} \cdot 3 m}$

Add parentheses.

$7 \sqrt{{(8 m^{4} n)}^{2} \cdot (3 m)}$

Step 2

Pull terms out from under the radical.

$7 (| 8 m^{4} n | \sqrt{3 m})$

Step 3

Remove non-negative terms from the absolute value.

$7 (8 m^{4} | n | \sqrt{3 m})$

Step 4

Multiply $8$ by $7$ .

$56 m^{4} | n | \sqrt{3 m}$