2. Rational Square Roots Lesson 9-3

3. 2 2 2 x 2 = 4

4. 3 x 3 = 9 3 3

5. 4 x 4 = 16 4 4

6. 5 5 5 x 5 = 25

7. The square root of 4 is 2

8. The square root of 9 is 3

9. The square root of 16 is 4

10. The square root of 25 is 5

11. You need to memorize at least the first 15 perfect squares.

12. Square root  1 = 1  4 = 2  9 = 3  16 = 4  25 = 5  36 = 6  49 = 7  64 = 8  81 = 9  100 = 10  121 = 11  144 = 12  169 = 13  196 = 14  225 = 15 Square root

13.  The is called the radical sign. The number under the radical is called the radicand. In,25 is the radicand. Radical Sign

14.  1.Simplify if you know the square root. 2.Use the Hockey Stick Method if necessary. Steps

15.  Factor Tree Method For every pair (square) you pull out 1.

16.  Hockey Stick For every pair (square) you pull out 1.

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21. Irrational Numbers Irrational numbers cannot be written as a fraction. They are non-terminating, non-repeating decimals. Example: √67

22. Find two consecutive whole numbers that the given square root is between. (Try to do this without using the table).  18  115  18 is between 4 and 5  115 is between 10 and 11  16 = 4 and  25 = 5 so  100 = 10 and  121 = 11 so

23. Steps for Simplifying 1. Look for perfect square factors using a factor tree. 2. Pull out all squares 3. Leave factors with no square root under the radical.

24. For every pair (square) you pull out 1.

27. Simplified Radical Form  18 =  9 2  = 99 22 3 22 =  108 =  36 3  =  36 33 6 33 =  96 =  16 6  =  16 66 4 66 = No factor inside the radical should be a perfect square.

34. Irrational Rational

35. Simplify the following expressions  49 7  64 + 9 -4-4   25 5 + =-2 =7 8 + 9 =56 + 9= 65  =5 5 + 7 =25 + 7= 32

36. Simplify the following expressions =  4 81 2 9 44  81 =  1 36  1 144 – = 1 6 1 12 – = 2 1 – = 1

37. Pop Quiz!!! Simplify lowest radical