What is the irrational cube root ^3√-24 rewritten as a product of an integer and another irrational cube root?(1 point)
Responses
2^3√3
2 root index 3 start root 3 end root
2^3√6
2 root index 3 start root 6 end root
−2^3√3
negative 2 root index 3 start root 3 end root
−2^3√4
negative 2 root index 3 start root 4 end root
Rewriting the irrational cube root ^3√-24 as a product of an integer and another irrational cube root, we get:
−2^3√3
To rewrite the irrational cube root ^3√-24 as a product of an integer and another irrational cube root, we need to find a perfect cube that can be factored out of -24.
First, let's find the prime factorization of 24: 24 = 2 * 2 * 2 * 3.
We can see that there are three 2's, which can be grouped together as 2 * 2 * 2 = 8, a perfect cube.
Therefore, we can rewrite ^3√-24 as ^3√8 * ^3√-3.
Simplifying further, ^3√8 = 2, so the rewritten expression is 2 * ^3√-3.
Therefore, the correct answer is 2 * ^3√-3.