To find the cubic root of \( 96 \), we want to calculate \( \sqrt[3]{96} \).
First, factor \( 96 \): \[ 96 = 2^5 \times 3^1 \]
Using the property that \( \sqrt[3]{a^m} = a^{m/3} \), we can break it down: \[ \sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} = \sqrt[3]{2^5} \times \sqrt[3]{3^1} \]
Calculating each piece:
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For \( \sqrt[3]{2^5} \): \[ \sqrt[3]{2^5} = 2^{5/3} = 2^{1 + 2/3} = 2 \times 2^{2/3} = 2 \cdot \sqrt[3]{4} \approx 2 \cdot 1.5874 \approx 3.1748 \]
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For \( \sqrt[3]{3^1} \): \[ \sqrt[3]{3^1} = 3^{1/3} \approx 1.44225 \]
Now combining these, we find: \[ \sqrt[3]{96} \approx 2 \cdot 1.5874 \cdot 1.44225 \approx 4.586 \]
So the final answer for the cubic root of \( 96 \) is approximately \( 4.586 \).
However, if you need the exact simplified form, we could also express it more simply: \[ \sqrt[3]{96} = 4 \cdot \sqrt[3]{6} \] since \( 4^3 = 64 \) and \( 96/64 = 1.5 = \frac{3}{2} \).
Ultimately, since your question appears to provide already calculated options, the most suitable response to match with the found value would be: \[ \sqrt[3]{96} \approx 4.586 \]
If you match it with any polynomial or option provided, please clarify or verify what specific choice might correlate to \( 4 \cdot \sqrt[3]{6} \).