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# how do i similify a nonperfect radical expression?

I do not understand this

### 2 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
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You first write down the radiant ( the number under radical ) as product of its prime facors.

Fundamental law of Arithmetic says that : Every Composite number consists of product of its prime factors:

4 = 2. 2 = 22

6 = 2 . 3

8 = 2.2 2 = 8

10 = 2 . 5

12 = 2 . 2 .3 = 22 . 3

14  = 2 . 7

16  = 2 4

18 = 2  . 32

20   =  22 . 5

We can multiply and divide the radicals, where the product and quotient to be a radical with product and quotient to be the product and quotient of the radicants  of radicants .

√a . √b  = √(ab)  ,         √a / √b = √(a/b) .

To simplify:   √(a2b ) = √a2 . √b = a √b

So To Simplify:

√12  = √( 22. 3 = 2 √3

√18 = √( 2 . 32) = 3√2

√(20) = √( 22 . 5 ) = 2 √5

√24 = √(22 . 6 ) = 2 √6

√28 = √22 .7 = 2 √7

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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