Simplify (19 square root of 9m^4)(4 square root of 10m^2)

$(19 \sqrt{9 m^{4}}) (4 \sqrt{10 m^{2}})$

Step 1

Rewrite $9 m^{4}$ as ${(3 m^{2})}^{2}$ .

$19 \sqrt{{(3 m^{2})}^{2}} (4 \sqrt{10 m^{2}})$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$19 (3 m^{2}) (4 \sqrt{10 m^{2}})$

Step 3

Simplify the expression.

Multiply $3$ by $19$ .

$57 m^{2} (4 \sqrt{10 m^{2}})$

Reorder $10$ and $m^{2}$ .

$57 m^{2} (4 \sqrt{m^{2} \cdot 10})$

Step 4

Pull terms out from under the radical.

$57 m^{2} (4 (m \sqrt{10}))$

Step 5

Multiply $m^{2}$ by $m$ by adding the exponents.

Move $m$ .

$57 (m \cdot m^{2}) (4 (\sqrt{10}))$

Multiply $m$ by $m^{2}$ .

Raise $m$ to the power of $1$ .

$57 (m^{1} m^{2}) (4 (\sqrt{10}))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$57 m^{1 + 2} (4 (\sqrt{10}))$

Add $1$ and $2$ .

$57 m^{3} (4 (\sqrt{10}))$

Step 6

Multiply $4$ by $57$ .

$228 m^{3} \sqrt{10}$