To multiply the expressions \(\sqrt{3m^2}\) and \(\sqrt{3}\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).
Thus we can write:
\[ \sqrt{3m^2} \cdot \sqrt{3} = \sqrt{3m^2 \cdot 3} \]
Next, we can multiply the terms inside the square root:
\[ = \sqrt{3 \cdot 3 \cdot m^2} = \sqrt{9m^2} \]
Now, we can simplify \(\sqrt{9m^2}\):
\[ \sqrt{9m^2} = \sqrt{9} \cdot \sqrt{m^2} = 3m \]
Therefore, the final answer is:
\[ 3m \]