1. Bell Work: Find the equation of the line that passes through the point (2,3) and has a slope of -2/5.

2. Answer: y = -2/5x + 19/5

3. LESSON 108: SQUARE ROOTS REVISITED, RADICAL EQUATIONS

4. The principal square root of a given positive number is that positive number which, multiplied by itself, yields the given number. Thus √2√2 = 2 √7√7 = 7 √3.14√3.14 = 3.14 Also (√2) = 2 (√7) = 7 (√3.14) = 3.14 2 2 2

5. It is necessary to remember that algebraic expressions represent particular real numbers that are determined by the values assigned to the variables. For example, (√x + 4) = x + 4(√x + 6) = x + 6 (√x + 3x + 5) = x + 3x + 5 2 2 2 4 2 2 4 2

6. There is only one number that will satisfy the equation x = 2, and that number is 2. if we replace x with 2 in this equation, we find 2 = 2 which is a true statement.

7. If we square both sides of the original equation, (x) = (2) x = 4 While the equation x = 2 had only one solution, the equation x = 4 has two numbers that satisfy it, the numbers +2 and -2. 2 2 2 2

8. We began with the equation x = 2, whose only solution is 2. we squared both sides and got the equation x = 4, which also has the number 2 as a solution but has another solution, which is the number -2. 2

9. It can be shown that if both sides of an equation are squared, all of the solutions to the original equation (if any exist) are also solutions to the resulting equation, but the reverse is not true, for all of the solutions of the resulting equation are not necessarily solutions of the original equation.

10. Example: Solve (√x – 2) + 3 = 0

11. Answer: x = 11 (√11 – 2) + 3 = 0 6 = 0 False The solution set of this equation is the empty set

12. Example: Solve (√x – 2) – 6 = 0

13. Answer: x = 38 0 = 0 x = 38 is a solution to the original equation

14. Example: Solve (√x + 9) – 5 = 0 2

15. Answer: x = 4 and -4 Both 4 and -4 are solutions to the equation

16. Example: Solve (√x – 1) – 3 + x = 0

17. Answer: x = 2 or x = 5 x = 2 is a solution to the original equation

18. Example: Solve (√2x – 3) = (√x + 2)

19. Answer: x = 5 is a solution of the original equation

20. HW: Lesson 108 #1-30