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# Why is it important to find nonperfect roots in radical form to simplify the process of performing basic operations with radical expressions?

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### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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"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".
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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If I understand the question correctly.

We can multiply and divide the radicals , but we can not add or subtract:

ie,  √3 . √2 = √6.

However:

√3 + √2  , can not yield to another radical with a given radicand  such as √5