Final answer:
To simplify √-288, factor 288 to 2² * 2² * 2² * 3², then take the square root to get 24, and multiply by i to express it in terms of imaginary numbers, resulting in 24i.
Step-by-step explanation:
To simplify √-288 in terms of imaginary numbers, we first identify that the square root of a negative number involves the imaginary unit, i, where i = √-1. Thus, √-288 can be written as √288 * √-1. Factoring 288, we get 288 = 2² * 2² * 2² * 3², so we can simplify √288 to 2 * 2 * 2 * 3 = 24. Therefore, the simplified form in terms of imaginary numbers is 24i.