Question

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

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

212−−√
2
12
2 start root 12 end root

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

46–√

Answer 1

To find the cubic root of \( 96 \), we can express it mathematically as \( \sqrt[3]{96} \).

Breaking down \( 96 \) into its prime factors:
\[
96 = 2^5 \times 3^1
\]

To find the cubic root, we can use the property that \( \sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b} \):
\[
\sqrt[3]{96} = \sqrt[3]{2^5 \times 3^1} = \sqrt[3]{2^5} \times \sqrt[3]{3}
\]

Now, we can find \( \sqrt[3]{2^5} \):
\[
\sqrt[3]{2^5} = 2^{5/3} = 2^{1 + 2/3} = 2 \times 2^{2/3} = 2 \sqrt[3]{4}
\]

Thus, combining our results, we get:
\[
\sqrt[3]{96} = 2 \sqrt[3]{4} \times \sqrt[3]{3} = 2 \sqrt[3]{12}
\]
where \( 12 = 4 \times 3 \).

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

If we evaluate the options given, the correct response is:
\[
2 \sqrt[3]{12}
\]