Question

Find the cubic root of 96.(1 point) Responses 212−−√ 2 start root 12 end root 27–√3 2 root index 3 start root 7 end root 212−−√3 2 root index 3 start root 12 end root 46–√ 4 start root 6 end root

Answer 1

To find the cubic root of 96, we write this as:

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

To simplify \( \sqrt[3]{96} \), we can factor 96 into its prime factors:

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

Now we can apply the cube root to these factors:

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

Next, we simplify each term:

1. \(\sqrt[3]{2^5} = 2^{5/3} = 2^{1 + 2/3} = 2 \times 2^{2/3}\), which can be written as \(2 \sqrt[3]{4}\).
2. \(\sqrt[3]{3^1} = 3^{1/3} = \sqrt[3]{3}\).

Combining these, we get:

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

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

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

Out of the given responses, the closest match is:

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

This is the answer.