Question

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

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

46–√
4 start root 6 end root

212−−√
2 start root 12 end root

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

Answer 1

To find the cubic root of 96, we can express 96 in a simpler form:

First, factor 96:
\( 96 = 2^5 \times 3^1 \)

Now, we can find the cubic root:
\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} = \sqrt[3]{2^5} \times \sqrt[3]{3^1} = 2^{5/3} \times 3^{1/3}
\]

We can break this down further:
\[
2^{5/3} = 2^{1 + 2/3} = 2 \times 2^{2/3} = 2 \sqrt[3]{4}
\]
\[
3^{1/3} = \sqrt[3]{3}
\]

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

Looking at the given responses, the answer corresponds to:
**2 \sqrt[3]{12}**

So the correct response is:
**2 \sqrt[3]{12}**.