To simplify the expression \( \sqrt{50} \cdot \sqrt{45} \), we can use the property of square roots that states \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \).
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First, calculate the product inside the square root: \[ 50 \cdot 45 = 2250 \]
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Now take the square root: \[ \sqrt{50} \cdot \sqrt{45} = \sqrt{2250} \]
Next, let's simplify \( \sqrt{2250} \):
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Factor 2250: \[ 2250 = 225 \cdot 10 = 15^2 \cdot 10 \]
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Now take the square root of the factors: \[ \sqrt{2250} = \sqrt{15^2 \cdot 10} = 15\sqrt{10} \]
Thus, the product \( \sqrt{50} \cdot \sqrt{45} \) in simplest radical form is \( 15\sqrt{10} \).
The answer is \( \boxed{15\sqrt{10}} \).