Question

Question
Find the cubic root of 96.(1 point)
Responses

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

27–√3
2 root index 3 start root 7 end root

46–√
4 start root 6 end root

212−−√

Answer 1

To find the cubic root of 96, we can express it as:

\[
\sqrt[3]{96}
\]

Next, we can simplify \(96\) to find its prime factorization:

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

Taking the cubic root of \(96\):

\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} = \sqrt[3]{2^5} \times \sqrt[3]{3^1} = \sqrt[3]{2^3 \cdot 2^2} \times \sqrt[3]{3} = 2 \times \sqrt[3]{4} \times \sqrt[3]{3}
\]

So, it can be rewritten as:

\[
2 \cdot \sqrt[3]{12}
\]

Therefore, the simplified expression for the cubic root of 96 is:

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

Among the given options, the closest matching response is:

**2 root index 3 start root 12 end root**.