what is the irrational cube root of

Question

(3 as index) √-24
rewritten as a product of an integer and another irrational cube root
A:2 (3 as index) √6
B:2 (3 as index) √3
C:-2 (3 as index) √3
D:-2 (3 as index) √4

Answer 1

To find the irrational cube root of (3 as index) √-24, we want to rewrite -24 as a product of a perfect cube and a remaining factor.

-24 = -2 * 2^3

So, the cube root of -24 = -2 * (3 as index) √2

Comparing this with the answer choices:

A: 2 (3 as index) √6 does not match the calculated value.
B: 2 (3 as index) √3 does not match the calculated value.
C: -2 (3 as index) √3 matches the calculated value.
D: -2 (3 as index) √4 does not match the calculated value.

The correct answer is C: -2 (3 as index) √3.