To find the cubic root of 96, we can express 96 in terms of its prime factors and then simplify.
The prime factorization of 96 is: \( 96 = 2^5 \times 3^1 \)
To find the cubic root (the cube root), we can write: \[ \sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} \] This can be simplified using the property of exponents: \[ \sqrt[3]{96} = \sqrt[3]{2^3 \times 2^2 \times 3^1} = \sqrt[3]{2^3} \cdot \sqrt[3]{2^2} \cdot \sqrt[3]{3} \] Since \( \sqrt[3]{2^3} = 2 \), we have: \[ \sqrt[3]{96} = 2 \cdot \sqrt[3]{4 \times 3} = 2 \cdot \sqrt[3]{12} \]
Therefore, the cubic root of 96 is: \[ 2 \sqrt[3]{12} \]
From the options given, the correct response is: 2 root index 3 start root 12 end root
So, the correct answer is: 2√12 (expressed as cubic root).
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