1. 6.1 Radical Expression Function and Models

2. Properties of Square Roots Every positive real number has two real-number square roots. The number 0 has just one square root, 0 itself. Negative numbers do not have real-number square roots. Square Root The number c is a square root of a if c 2 = a.

3. 1)Find the square roots of 9 Answer: 3 and -3 2)Find the square roots of 36 Answer: 6 and -6 3)Find the square roots of 1 Answer: 1 and -1 4)Find the square roots of -16 Answer: none because no real number square gives -16 Examples

4. principal square root (non-negative square root) is the radical sign and a is the radicand Example 1) 5= 0.2= -4-4= 10=

5. Example Find principal square roots and simplify. Slide 5

6. Examples

7. More examples 6) 7) 8) You may have to use calculator if the radicand is not a perfect square 9) f(x) = Find f(0) = f(3)= f(-5)= =0 = 3.32 No real answer

8. 10) f(x) = 3x + 12 a)Find f(-1) = 3(-1) + 12 = -3 + 12 = 9 = 3 b)Find f(x+1) = 3(x+1) + 12 = 3x + 3 + 12 = 3x + 15

9. For any real number The principal (nonnegative) square root of a 2 is the absolute value of a. Principle Square Root of a 2

11. Radical Expressions and Functions Cube Root

12. Find cube roots, simplifying certain expressions, and find outputs of cube-root functions. = 2 because 2 3 =8

13. For any real number : a) when k is an even natural number. Use absolute value when k is even unless a is nonnegative. b) when k is an odd natural number greater than 1. Do not use absolute value when k is odd. Slide 13

14. Ex: 1)g(x) = 3 x – 3 Find g(-24) = 3 -24 – 3 = 3 -27 = -3 2) 5 -32 = = -2 3) 9 (x + 1) 9 = = x + 1

15. 4) 4 81x 4 = = | 3x | = 3 | x | 5)Find the domain of Look at the graph using G.C. Domain: x + 5 ≥ 0 x≥ -5 [-5, ∞)

16. 6)2x – 5 - 3 Domain is 2x – 5 ≥ 0 2x ≥ 5 x ≥ 5/2 [5/2, ∞)