To solve the expression \( \sqrt[3]{\frac{0.0072 \times 81.3^2}{\sqrt{23140}}} \), we need to perform it step by step.
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Calculate \( 81.3^2 \): \[ 81.3^2 = 6616.89 \]
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Now calculate \( 0.0072 \times 6616.89 \): \[ 0.0072 \times 6616.89 \approx 47.7404 \]
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Next, calculate \( \sqrt{23140} \): \[ \sqrt{23140} \approx 152.67 \quad (\text{using a calculator}) \]
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Now, divide the result from step 2 by the result from step 3: \[ \frac{47.7404}{152.67} \approx 0.3127 \]
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Finally, calculate the cube root: \[ \sqrt[3]{0.3127} \approx 0.681 \]
So, the final answer is approximately: \[ \sqrt[3]{\frac{0.0072 \times 81.3^2}{\sqrt{23140}}} \approx 0.681 \]
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