To simplify the expression \(\sqrt{5x^2} \times \sqrt{15x}\), we can use the property of square roots that states \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\).
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Combine under the square root: \[ \sqrt{5x^2} \times \sqrt{15x} = \sqrt{5x^2 \times 15x} \]
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Multiply the expressions inside the square root: \[ 5x^2 \times 15x = 75x^3 \]
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Now we have: \[ \sqrt{75x^3} \]
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Factor \(75\) into \(25 \times 3\) to extract the square root: \[ \sqrt{75x^3} = \sqrt{25 \times 3 \times x^2 \times x} = \sqrt{25} \times \sqrt{3} \times \sqrt{x^2} \times \sqrt{x} \]
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Simplify the square roots:
- \(\sqrt{25} = 5\),
- \(\sqrt{x^2} = x\).
Thus, we have: \[ \sqrt{75x^3} = 5 \times \sqrt{3} \times x \times \sqrt{x} = 5x\sqrt{3x} \]
The final simplified expression is: \[ \boxed{5x\sqrt{3x}} \]
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