1. EXAMPLE 3 Use properties of radicals Use the properties of radicals to simplify the expression. a.12 3 18 3 12 8 3 =216 3 = =6 Product property b. 80 4 5 4 5 4 = = 16 4 = 2 Quotient property

2. EXAMPLE 4 Write radicals in simplest form Write the expression in simplest form. a. 135  3 = 27  3 5 =  3 5  3 5  3 3 = Factor out perfect cube. Product property Simplify.

3. EXAMPLE 4 Write radicals in simplest form 28  5 2 = Simplify. b. 7  5 8  5 7  5 8  5 4  5 4  5 = Make denominator a perfect fifth power. 32  5 28  5 = Product property

4. EXAMPLE 5 Add and subtract like radicals and roots Simplify the expression. a. 10  4  4 7 + =  4 (1 + 7) = 10  4 8 b. (8 1/5 ) 2 + 10 = (8 1/5 )(2 +10) = (8 1/5 ) 12 2  3 32  3 – = c. 54  3 – 2  3 =2  3 27  3  2 3 – 2  3 (3 – 1) = = 22  3

5. GUIDED PRACTICE for Examples 3, 4, and 5 Simplify the expression. 27 4 3 4 27 3 4 =81 4 = =3 Product property SOLUTION 6. 27 4 3 4

6. Simplify. Factor out numerator to perfect cube. Product property GUIDED PRACTICE for Examples 3, 4, and 5 SOLUTION 7. 2  3 250  3 = 2  3 5353  3 2  3 = 5 = 2  3 5353  3 2 2  3  3

7. GUIDED PRACTICE for Examples 3, 4, and 5 24  5 2 = Simplify. 3  5 4  5 8  5 8  5 = Make denominator a perfect fifth power. 32  5 24  5 = Product property SOLUTION 3 4 5 8. 3 4 5

8. GUIDED PRACTICE for Examples 3, 4, and 5 SOLUTION 9. 5  3 40  3 + 5  3  3 +  = 5  3 2 3 5 3 + = 5  3 +2 5  3 = 5  3 (1+ 2) 3 5  3 =