Coleman Best
07/24/2024 · Elementary School
Perform the operations and simplify. \( \frac{\sqrt{3 x^{3}}}{\sqrt{5 x}} \cdot \sqrt{15 x^{4}} \) \( \sqrt{9 x^{6}} \) \( 9 x^{6} \) \( 3 x^{3} \) \( 3 x^{2} \sqrt{x^{3}} \)
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Step-by-step Solution
Calculate or simplify the expression \( \frac{\sqrt{3x^3}}{\sqrt{5x}} \cdot \sqrt{15x^4} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\sqrt{3x^{3}}}{\sqrt{5x}}\times \sqrt{15x^{4}}\)
- step1: Simplify the root:
\(\frac{x\sqrt{3x}}{\sqrt{5x}}\times \sqrt{15x^{4}}\)
- step2: Divide the terms:
\(\frac{\sqrt{3}\times x}{\sqrt{5}}\times \sqrt{15x^{4}}\)
- step3: Simplify the root:
\(\frac{\sqrt{3}\times x}{\sqrt{5}}\times \sqrt{15}\times x^{2}\)
- step4: Rewrite the expression:
\(\frac{\sqrt{3}\times x}{\sqrt{5}}\times \sqrt{5}\times \sqrt{3}\times x^{2}\)
- step5: Reduce the fraction:
\(\sqrt{3}\times x\sqrt{3}\times x^{2}\)
- step6: Calculate the product:
\(3x\times x^{2}\)
- step7: Multiply the terms:
\(3x^{3}\)
The simplified expression is \(3x^{3}\).
Quick Answer
The simplified expression is \(3x^{3}\).
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