To simplify the expression \(\sqrt{50} \cdot \sqrt{45}\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).
First, we multiply the numbers inside the square roots:
\[ \sqrt{50} \cdot \sqrt{45} = \sqrt{50 \cdot 45} \]
Calculating \(50 \cdot 45\):
\[ 50 \cdot 45 = 2250 \]
Now, we have:
\[ \sqrt{50} \cdot \sqrt{45} = \sqrt{2250} \]
Next, we simplify \(\sqrt{2250}\). We start by factoring \(2250\):
\[ 2250 = 225 \cdot 10 = 15^2 \cdot 10 \]
So we have:
\[ \sqrt{2250} = \sqrt{15^2 \cdot 10} = \sqrt{15^2} \cdot \sqrt{10} = 15\sqrt{10} \]
Thus, the product in simplest radical form is:
\[ \boxed{15 \sqrt{10}} \]