NEED HELP ASAP!!
"Why is it important to find nonperfect roots in radical form to simplify the process of performing basic operations with radical expressions?"
A "nonperfect" root must mean the root of a number that is not a perfect square.
Consider E = √(48) + √(175) - √(63). How would you simplify it?
First factorize each radicand into its prime factors:
E = √(2*2*2*3*3) + √(5*5*7) - √(3*3*7)
Every pair of identical primes under a radical represents a perfect square and can be replaced by one of those primes as a factor outside of the radical. Do that until there are no more pairs of primes under the radical and the radical that's left is a "nonperfect root".
E = 2*3*√(2) + 5*√(7) - 3*√(7)
And now you can identify and combine any "like terms":
E = 6√(2) + 2√(7)
So the short answer to the question is, "to identify and combine like terms".