1. High School Common Core Number & Quantity The Real Number System – Use properties of rational and irrational numbers.  Means there is a note to read at the bottom of the slide.

2. Simplifying Radicals Radical (also called a square root) A number that, when multiplied by itself, will give back that number. You “undo” an exponent with a radical. x= x  = x 2 x 3= 3  = 93

3. Index The number written outside the radical denoting its inverse power. 2 49=7272 = 7 3 27=3 = 3 4 16=2424 = 2 3 4

4. Perfect Squares 11 24 39 416 525 636 749 864 981 10100 The numbers that give you a whole number when you take their square root.

5. Determine = 416

6. Determine = 9 81

7. Determine = 11121 

8. Determine = 15225

9. Determine = 20400

10. Ex1:  Determine the perfect square factor. Explain Simplify   Write both factors with radicals (perfect square goes 1 st ).  Take the square root of the perfect square. 75 25 3 5 3

11. Simplify 45 9 5 3 5

12. Simplify 24 4 6 2 6

13. Simplify 50 25 2 5 2

14. Simplify 98 49 2 7 2

15. Ex3:  Determine the perfect square factor. Explain Simplify   Bring down the number outside the radical.  Take the square root of the perfect square and multiply it by outside number. 12 4 3 -5 3  2 -10 3 -5  Write both factors with radicals.

16. Simplify 27 9 3 4 3  3 -12 3 4 4

17. Simplify 125 25 5 -3 5  5 -15 5 -3

18. Simplify 36  6 -48 -8 

19. Simplify 40 4 10 7  2 14 10 7 7

20. Ex3:  Determine the LARGEST perfect square factor. ExplainSimplify   Write both factors with radicals.  Take the square root of the perfect square. 72 36 2 6 2  If number inside radical can be divided by a perfect square keep simplifying.

21. Ex3:  Determine the LARGEST perfect square factor. ExplainSimplify   Write both factors with radicals.  Take the square root of the perfect square.  If number inside radical can be divided by a perfect square keep simplifying. 72 9 8 3 8 3 4 2 3  2 2 6 2

22. 48 4 12 2 2 4 3 2  2 3 4 3 Simplify 48 16 3 4 3 

23. 128 16 8 4 8 4 4 2 4  2 2 8 3 Simplify 128 64 2 8 2

24. 80 4 20 2 2 4 5 2  2 5 4 5 Simplify 80 16 5 4 5

25. Simplify 200 100 2 -5 2  10 -10 2 -5

26. Simplify 108 36 3 7 3  6 42 3 7 7

27. Simplify 81  9 -3 -27

28. Tips for the lesson  Have students record vocabulary and examples in their notes. They should do guided practice on scratch paper or on whiteboards. If you want to grade guided practice as part of their classwork grade have them staple it and hand it in with their classwork or homework. Use guided practice time to call on students and assess the class.  There are multiple ways to teach this including using a factor tree. I like the table method the best because students eventually memorize their perfect squares and stop having to reference the table. Also, I believe students can’t affectively use a factor tree when doing more complex problems such as adding, subtracting, multiplying, and dividing expressions with multiple radicals.  I allow students to use calculators with this lesson so they can figure out how to use the square root sign on the calculator. Also, allows them to radicals with larger numbers and they use it to guess & check perfect square factors. Eventually, like the table of perfect squares, students stop needing to use the calculator as they get more comfortable.  Some students have a difficult time with this topic and giving lots of practice and feedback when they make mistakes will help. The class as a whole will get better as you build on this with each lesson.