To find the cubic root of 96, we first express it in a more manageable form. The cubic root of a number \( x \) is denoted as \( \sqrt[3]{x} \).
We can simplify \( \sqrt[3]{96} \) as follows:
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Factor 96 into its prime factors: \[ 96 = 2^5 \times 3^1 \]
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Using the property of cubic roots, we can write: \[ \sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} = \sqrt[3]{2^5} \times \sqrt[3]{3^1} \]
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Now we can simplify each part:
- For \( \sqrt[3]{2^5} \), we can separate this as: \[ \sqrt[3]{2^5} = \sqrt[3]{(2^3) \cdot (2^2)} = \sqrt[3]{2^3} \cdot \sqrt[3]{2^2} = 2 \cdot \sqrt[3]{4} \]
- For \( \sqrt[3]{3^1} \), this remains \( \sqrt[3]{3} \).
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Thus, \[ \sqrt[3]{96} = 2 \cdot \sqrt[3]{4} \cdot \sqrt[3]{3} = 2 \cdot \sqrt[3]{12} \]
The final result is: \[ \sqrt[3]{96} = 2 \cdot \sqrt[3]{12} \]
Given the options, the correct response is: \( 2 \sqrt[3]{12} \).