Find the cubic root of 96.(1 point)

Question

Responses

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

212−−√
2 start root 12 end root

46–√
4 start root 6 end root

212−−√3

Answer 1

To find the cubic root of 96, we can express 96 as \( 2^5 \times 3^1 \).

Now we calculate the cubic root:

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

Breaking this down further:

\[ \sqrt[3]{2^5} = 2^{5/3} = 2^{1 + 2/3} = 2 \cdot 2^{2/3} = 2 \cdot \sqrt[3]{4} \]

And

\[ \sqrt[3]{3^1} = 3^{1/3} \]

Putting it all together:

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

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

Among the given responses, the one that matches this result is:

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