To simplify the expression \(\sqrt{50} \cdot \sqrt{45}\), we start by combining the square roots:
\[ \sqrt{50} \cdot \sqrt{45} = \sqrt{50 \cdot 45} \]
Now, we calculate \(50 \cdot 45\):
\[ 50 \cdot 45 = 2250 \]
Thus, we have:
\[ \sqrt{50 \cdot 45} = \sqrt{2250} \]
Next, we simplify \(\sqrt{2250}\). We can factor \(2250\) as follows:
\[ 2250 = 225 \cdot 10 \]
We know that:
\[ 225 = 15^2 \]
So we can express \(\sqrt{2250}\) as:
\[ \sqrt{2250} = \sqrt{225 \cdot 10} = \sqrt{225} \cdot \sqrt{10} = 15\sqrt{10} \]
Thus, the simplest radical form of the original expression \(\sqrt{50} \cdot \sqrt{45}\) is:
\[ \boxed{15\sqrt{10}} \]