Find the cubic root of 96.(1 point)

Responses

46–√
4 start root 6 end root

212−−√
2 start root 12 end root

212−−√3
2 root index 3 start root 12 end root

27–√3

1 answer

To find the cubic root of \( 96 \), we can express \( 96 \) in terms of its prime factors:

\[ 96 = 2^5 \times 3^1 \]

Next, to find the cubic root, we take the cube root of each factor:

\[ \sqrt[3]{96} = \sqrt[3]{2^5} \times \sqrt[3]{3^1} \]

Calculating each component separately:

\[ \sqrt[3]{2^5} = 2^{5/3} = 2^{1 + 2/3} = 2 \cdot 2^{2/3} = 2 \sqrt[3]{4} \] \[ \sqrt[3]{3^1} = 3^{1/3} \]

Putting them together, we have:

\[ \sqrt[3]{96} = 2 \sqrt[3]{4} \times \sqrt[3]{3} = 2 \sqrt[3]{12} \]

Thus, the cubic root of \( 96 \) can be expressed as:

\[ \sqrt[3]{96} = 2 \sqrt[3]{12} \]

Therefore, the answer to the question is:

\( 2 \sqrt[3]{12} \)