Question

What is the irrational cube root −24−−−−√3
−
24
3
rewritten as a product of an integer and another irrational cube root?(1 point)
Responses

−23–√3
−
2
3
3
negative 2 root index 3 start root 3 end root

23–√3
2
3
3
2 root index 3 start root 3 end root

26–√3
2
6
3
2 root index 3 start root 6 end root

−24–√3

Answer 1

To rewrite the expression \( -\sqrt[3]{24} \) as a product of an integer and another irrational cube root, we can start by factoring 24 into its prime factors.

The prime factorization of 24 is:
\[
24 = 8 \times 3 = 2^3 \times 3
\]

Now, we take the cube root:
\[
-\sqrt[3]{24} = -\sqrt[3]{8 \times 3} = -\sqrt[3]{8} \cdot \sqrt[3]{3} = -2 \cdot \sqrt[3]{3}
\]

Thus, we can rewrite \( -\sqrt[3]{24} \) as:
\[
-2 \sqrt[3]{3}
\]

So the answer is:
**\(-2 \sqrt[3]{3}\)**.