What is the irrational cube root ^3√-24 rewritten as a product of an integer and another cube root?
To rewrite the irrational cube root ^3√-24 as a product of an integer and another cube root, we need to find a cube root of -24 that is a rational number.
Let's find the prime factorization of -24: -24 = -1 * 2^3 * 3.
The prime factorization contains one cube, which is 2^3 = 8.
Rewriting -24 as a product of an integer and another cube root:
^3√-24 = ^3√(8 * -3) = ^3√8 * ^3√-3 = 2 * ^3√-3.
Therefore, the irrational cube root ^3√-24 can be rewritten as the product of the integer 2 and the cube root ^3√-3: 2 * ^3√-3.