(5sqrt (27x))(sqrt (75x)) 3. 225x 125x 75sqrt (3x)

To simplify the expression \((5\sqrt{27x})(\sqrt{75x})\), we can follow these steps:<br /><br />1. Simplify each square root term:<br /> \[<br /> \sqrt{27x} = \sqrt{9 \cdot 3x} = \sqrt{9} \cdot \sqrt{3x} = 3\sqrt{3x}<br /> \]<br /> \[<br /> \sqrt{75x} = \sqrt{25 \cdot 3x} = \sqrt{25} \cdot \sqrt{3x} = 5\sqrt{3x}<br /> \]<br /><br />2. Substitute the simplified terms back into the original expression:<br /> \[<br /> (5\sqrt{27x})(\sqrt{75x}) = (5 \cdot 3\sqrt{3x})(5\sqrt{3x})<br /> \]<br /><br />3. Multiply the constants and the square root terms:<br /> \[<br /> 5 \cdot 3 \cdot 5 \cdot \sqrt{3x} \cdot \sqrt{3x} = 75 \cdot (\sqrt{3x})^2 = 75 \cdot 3x = 225x<br /> \]<br /><br />Therefore, the simplified expression is:<br />\[<br />225x<br />\]<br /><br />So, the correct answer is:<br />\[<br />225x<br />\]