Question

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

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

212−−√3

Answer 1

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

Starting with \( 96 \):
\[
96 = 2^5 \times 3^1
\]

The cubic root of a number can be calculated using the following property:
\[
\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}
\]

Applying this property:
\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} = \sqrt[3]{2^5} \times \sqrt[3]{3^1}
\]

We can split \( 2^5 \) into \( 2^3 \times 2^2 \) to simplify:
\[
\sqrt[3]{2^5} = \sqrt[3]{2^3} \times \sqrt[3]{2^2} = 2 \times \sqrt[3]{4}
\]
Thus:
\[
\sqrt[3]{96} = 2 \times \sqrt[3]{4} \times \sqrt[3]{3} = 2 \times \sqrt[3]{12}
\]

So the cubic root of \( 96 \) simplifies to:
\[
\sqrt[3]{96} = 2 \sqrt[3]{12}
\]

Now looking at your provided responses, we can see that the correct response is:

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