Solving Equations with a Radical: Find the Value of "a

1. 1.) 50 2.) 32 3.) 80 4.) 128 Bellwork 5 2 4 2 4 5 8 2

2. Solving Equations with a radical Solve for a • 1.) a2 = 36 • 2.) a2 = 49 • 3.) a2 = 60 • 4.) a2 = 80

3. Solving Equations with a radical Solve for a • 1.) a2 = 36 • a = 36 • a = 6, or -6

4. Solving Equations with a radical Solve for a • 2.) a2 = 49 • a = 49 • a = 7, or -7

5. Solving Equations with a radical Solve for a • 3.) a2 = 60 • a = 60 • a = 2 15, or -2 15

6. Solving Equations with a radical Solve for a • 4.) a2 = 80 • a = 80 • a = 4 5 , or -4 5

7. Objective • To be able to use the Pythagorean Theorem to find the lengths of the sides of a Right Triangle.

8. Area of a Square • Area = Length * Width Length = 4 Width = 4 Area = 16

9. Areas of 3 squares 3 X 3 4 X 4 5 X 5

10. Arrange them into a triangle 5 X 5 4 X 4 3 X 3

11. Now make your squares First Draw the Squares on your paper • Cut out 3 squares that are: • 1.) 3,4,5 in length Arrange the sides so they form a Right Triangle.

12. Pythagorean Theorem • In the 3,4,5 triangle add up the areas of the 2 smallest squares and compare that to the area of the largest square.

13. Pythagorean Theorem • Area =16 Area = 25 9 + 16 = 25 Area = 9

14. Now do #2 and #3. Now make your squares First Draw the Squares on your paper • Outline 3 squares that are: • 1.) 3,4,5 in length • 2.) 6,8,10 in length • 3.) 6,7,8 in length

15. Pythagorean Theorem2.) 6,8,10 in length Area =36 Area = 100 36 + 64 = 100 Area = 64

16. Pythagorean Theorem3.) 6,7,8 in length Area =49 Area = 64 36 + 49 = 64 Area = 36

17. Pythagorean Theorem • What did you find????

18. Pythagorean Theroem • The sum of the areas of the 2 smaller squares equals the area of the largest square. • This is TRUE for all Right Triangles a2 + b2 = c2

19. Pythagorean Theorem • Area =a2 Area = c2 c a a2 + b2 = c2 b Area = b2

20. 1.) a=6, b= 8 2.) 82+152=c2 Find c if a2 + b2 = c2

21. 1.) Find the Hypotenuse • a2 + b2 = c2 • 62 + 82 = c2 • 36 + 64 = c2 • 100 = c2 • 10 = c

22. 2.) Find the Hypotenuse • a2 + b2 = c2 • 82 + 152 = c2 • 64 + 225 = c2 • 289 = c2 • 17 = c

23. 3.) a=12,b=16 4.) 72+242=c2 Find c if a2 + b2 = c2 Now you do these

24. 3.) Find the Hypotenuse • a2 + b2 = c2 • 122 + 162 = c2 • 144 + 256 = c2 • 400 = c2 • 20 = c

25. 4.) Find the Hypotenuse • a2 + b2 = c2 • 72 + 242 = c2 • 49 + 576 = c2 • 625 = c2 • 25 = c

26. Pythagorean Theorem • What relationship exists between the lengths of the sides of a Right Triangle??

27. Pythagorean Theorem • In a Right Triangle, the sum of the smallest sides squared is equal to the largest side squared. • a2 + b2 = c2 where c is the longest side • The longest side is known as the hypotenuse of the triangle.

28. Pythagorean Theorem • a2 + b2 = c2 • 32 + 42 = 52 • 9 + 16 = 25 • 25 = 25 • Where sides (a & b) are the shortest sides and side c is the hypotenuse.

29. Find a if b = 8 & c = 10 • a2 + b2 = c2 • a2 + 82 = 102 • a2 + 64 = 100 • a2 + 64 - 64 = 100 - 64 • a2 = 36 a = 6

30. 1.) c=10, b= 8 2.) c=20,b=16 3.) a2+152=172 4.) a2+242=252 Find a if a2 + b2 = c2

31. 1.) Find a • a2 + b2 = c2 • a2 + 82 = 102 • a2 + 64 = 100 • a2 = 36 • a = 6

32. 2.) Find a • a2 + b2 = c2 • a2 + 162 = 202 • a2 + 256 = 400 • a2 = 144 • a = 12

33. 3.) Find a • a2 + b2 = c2 • a2 + 152 = 172 • a2 + 225 = 289 • a2 = 64 • a = 8

34. 4.) Find a • a2 + b2 = c2 • a2 + 242 = 252 • a2 + 576 = 625 • a2 = 49 • a = 7

35. 1.) c=10, b= 8 2.) c=20,b=16 3.) a2+152=172 4.) a2+242=252 1.) a=6 2.) a=12 3.) a=8 4.) a=7 Find a if a2 + b2 = c2

36. Expression with radicals • Evaluate b2 - 4acWhen a =1, b= -2, c=-3 • (-2)2 - 4(1)(-3) • 4 + 12 = 16 = 4

37. Expression with radicals • Evaluate b2 - 4acWhen a =4, b= 5, c=1 • (5)2 - 4(4)(1) • 25 - 17 • 9 = 3 Your Turn

38. Classwork • Worksheet 9.1 • homework: • page 455 (7-34)