1. 1.1 S IMPLIFYING R ADICALS Sec Math 2

2. S IMPLIFYING R ADICALS

3. Methods for Simplifying Radical Expressions Two Methods for Simplifying Radical Expressions: 1. Simplify by finding perfect squares 2. Simplify by creating a factor tree

4. 1. Simplify by finding perfect squares

5. P ERFECT S QUARES 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324 400 625 289

6. = 2 = 4 = 5 = 10 = 12

7. = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

8. = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

9. 2. Simplify by creating a factor tree

10. Step 1. Factor the number under the radical sign into prime numbers 48 = 2 ∙ 24 2 ∙ 12 2 ∙ 6 2 ∙ 3 Prime numbers of 48 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 Simplify or Reduce a Radical by Finding Prime Factors Reduce

11. Step 2. Group prime numbers into squares Step 3. Reduce the radical from the perfect squares Step 4. Simplify the radical. Simplify or Reduce a Radical by Finding Prime Factors

12. Simplify Each Expression Simplify Method 1: Finding Perfect Squares Method 2: Factor into Prime Numbers

13. A radical expression is in simplest form when all the following are true.

14. Simplify or Reduce a Radical Simplify the expression

15. = X = Y 3 = P 2 X 3 Y = 2X 2 Y = 5C 4 D 10

16. = = = =

17. = = = =

18. Please Do you homework Worksheet: 1.1 Simplifying Radicals