1. 11.2A Simplify and Multiply Square Roots

2. Squaring a Number When a number is squared, it is multiplied to itself: 1 5525 -3 9 Notice squaring any number always results in a ___________________ number. positive

3. Taking the Square Root of a Number Just as subtracting is the opposite of adding and dividing is the opposite of multiplying, the opposite of squaring is ____________ ______________. squarerooting

4. Ex 1: Find the square roots of the following numbers: 3 1 23 m Not possible!

5. Ex 2: Find the following: (Think of the negative sign in front as just being negative one multiplied to the positive root.) –5 –23

6. –m –x

8. x2x2 2 y3y3

9. Factor tree inside radical Circle any pairs Multiply pairs w/ # in front Multiply loners back inside

10. Ex 4: Simplify a) 5 4 2 2 =2 5

11. 2 36 6 6 23 23 b) = 6 2

12. Ex 4: Simplify c) 2 25 5 5 x x =5 2 x

13. Ex 4: Simplify d) 2 12 2 6 2 3 x x x x x x =2 6 x3x3

14. Ex 4: Simplify e) 2 9 3 3 x x = 6 2 x

15. Ex 4: Simplify f) 3 4 2 2 =10 3 y8y8

16. = g) 70 x5x5

17. h) 5 8 42 22 = 6 10 y4y4

18. Multiply #s in front Multiply #s inside Factor tree and simplify

19. 2 35

20. 5 49 77 =35

21. 20x 2 5 4 2 2 = 2 5 x

22. 240y 10 24 10 6 4 3 2 2 2 2 5 = 4 15 y5y5

23. 6 5t 6 = 6 5 t3t3

24. 14 12k 8 4 3 2 2 = 28 3 k4k4

25. Divide exponent by 2 Leave remainder 1 inside

26. x x x = x x

27. = 4 p p2p2

28. 6 4 3 2 2 2 = 2 6k k9k9

29. 8 4 4 2 2 2 2 2 = 20 2w w7w7

30. 6 6 = 6 p p3p3

31. 7 4 2 2 = 2 7x x7x7

32. 63y 5 9 7 3 3 = 3 7y y2y2

33. 80d 5 8 10 4 2 2 2 2 5 = 4 5d d2d2

34. 150x 7 15 10 3 5 5 2 = 5 6x x3x3

35. 243x 13 27 9 9 3 3 3 3 3 = 9 3x x6x6