Simplify square root of 6m* square root of 3m

$\sqrt{6 m} \cdot \sqrt{3 m}$

Step 1

Multiply $\sqrt{6 m} \sqrt{3 m}$ .

Combine using the product rule for radicals.

$\sqrt{6 m (3 m)}$

Multiply $3$ by $6$ .

$\sqrt{18 m \cdot m}$

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

$\sqrt{18 (m^{1} m)}$

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

$\sqrt{18 (m^{1} m^{1})}$

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

$\sqrt{18 m^{1 + 1}}$

Add $1$ and $1$ .

$\sqrt{18 m^{2}}$

Step 2

Rewrite $18 m^{2}$ as ${(3 m)}^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2) m^{2}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 m^{2}}$

Move $2$ .

$\sqrt{3^{2} m^{2} \cdot 2}$

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

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

Step 3

Pull terms out from under the radical.

$3 m \sqrt{2}$