RADICAL EXPRESSIONS

1. RADICAL EXPRESSIONS

2. RADICAL EXPRESSIONS ARE THE SAME AS SQUARE ROOTS

3. Radical Expressions • Square Roots & Perfect Squares • Simplifying Radicals • Multiplying Radicals • Dividing Radicals • Adding Radicals

4. What is the square root? 64

5. The square root of a number is a # when multiplied by itself equals the number 64 8 8

6. What is the square root? X2

7. A Square Root is a term when squared is the Perfect Square X2 X X

8. What is the square root? 64x2

9. Answer 64x2 8x 8x

10. What is the square root? 4x2

11. Answer 4x2 2x 2x

12. What is the square root? (x+3)2

13. Answer (x+3) (x+3)2 (x+3)

14. Radical Sign • This is the symbol for square root • If the number 3 is on top of the v, it is called the 3rd root.

15. Radical Sign • This is the 4th root. • This is the 6th root • If n is on top of the v, it is called the nth root.

16. Cube Root If the sides of a cube are 3 inches Then the volume of the cube is 3 times 3 times 3 or 33 which is 27 cubic inches.

17. NUMBER Perfect Squares Numbers that are perfect squares are: 12=1, 22= 4, 32= 9, 42= 16, 52= 25, 62= 36, 72= 49, 82= 64, 92= 81, 102= 100, …

18. Recognizing Perfect Squares(NAME THE SQUARE ROOTS) Variables that are perfect squares are: x2, a4, y22, x100… (Any even powered variable is a perfect square) x25 EVEN POWERED EXPONENTS ARE SQUARES x25 x50

19. NAME THE SQUARE ROOT 9x50

20. 3x25 EVEN POWERED EXPONENTS ARE SQUARES 3x25 9x50

21. Recognizing Perfect Squares(NAME THE SQUARE ROOTS) x2 4 25x2 4x6

22. Recognizing Perfect Squares(NAME THE SQUARE ROOTS) x 2 x x2 2 4 5x 2x3 5x 25x2 2x3 4x6

23. Simplifying Square Roots

24. Simplifying Square Roots We can simplify if 8 contains a Perfect Square

25. Simplifying Square Roots Look to factor perfect squares (4, 9, 16, 25, 36…) Put perfect squares in first radical and the other factor in 2nd. Take square root of first radical

26. Simplifying Square Roots

27. Simplifying Square Roots 1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (Put perfect squares in first radical and other factor in 2nd)

28. Simplifying Square Roots 1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical

29. Simplifying Square Roots 1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical

30. Simplifying Square Roots 1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical

31. Simplifying Square Roots

32. Simplifying Square Roots 1. Factor any perfect squares (4, 9, 16, 25, 36…) (& Put perfect squares in first radical and other factor in 2nd)

33. Simplifying Square Roots 1. Factor any perfect squares (4, 9, 16, 25, 36…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical

34. Simplifying Square Roots 1. Factor any perfect squares (4, 9, 16, 25, 36…) (& Put perfect squares in first radical and other factor in 2nd)

35. Simplifying Radicals 1. Factor any perfect squares (4, 9, 16, 25, 36…) (& Put perfect squares in first radical and other factor in 2nd)

36. Simplifying Radicals 1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical

37. Simplifying Fraction Radicals

38. Simplifying Fraction Radicals 1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd)

39. Simplifying Fraction Radicals 1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical

40. Simplifying Fraction Radicals 1. Factor any perfect squares (4, 9, 16, 25, x2, y6…) from NUMERATOR & DENOM. (& Put perfect squares in first radical and other factor in 2nd) 2. Take square root of first radical 3. REDUCE

41. Finding Perfect Squares The most common perfect squares are 4 & 9. USE DIVISIBILITY RULES: A number is divisible by 4 if the last 2 digits are divisible by 4. ( 23,732 is divisible by 4 since 32 is.) A number is divisible by 9 if the sum of it’s digits are. (4653 is divisible by 9 since the sum of it’s digits are.)

42. Finding Perfect Squares MORE EASY TO FIND PERFECT SQUARES: A number with an even number of Zeros. ( 31,300 is divisible by 10, 70,000 is divisible by 100) A number ending in 25, 50 or 75 is divisible by 25. (425 & 350 & 775 are all divisible by 25)

43. Perfect Squares Guide Divisibility Rules for Perfect Squares 4: If Last 2 Digits are Divisible by 4 9: If Sum of Digits are Divisible by 9 16: Use 4 Rule 25: If # ends in 25, 50, 75 or 00 36: Use 4 or 9 Rule 49: Look for multiple of 50 and subtract multiple 64: Use 4 Rule 81: Use 9 Rule 100: If # ends in 00 121: No Rule, Divide # by 121 144: Use 4 or 9 Rule

45. Multiply Radicals

46. Multiply Radicals Multiply to one radical

47. Multiply Radicals Multiply to one radical

48. Multiply Radicals Multiply to one radical Simplify • Factor any perfect squares (4, 9, 16, x2, y6…)

49. Multiply Radicals Multiply to one radical Simplify • Factor any perfect squares (4, 9, 16, x2, y6…)

50. Multiply Radicals Multiply to one radical Simplify • Factor any perfect squares (4, 9, 16, x2, y6…) • Take square root of first radical