1. Vocabulary Unit 4 Section 1:
1. Real number : the set of all numbers that can be expressed as a decimal or that are on the number line. Real numbers have certain properties and different classifications, including natural, whole, integers, rational and irrational. 2. Irrational number- real numbers that cannot be represented as terminating or repeating decimals. Example ∏, e, √2 3. Rational number: A number expressible in the form a/b or – a/b for some fraction a/b. The rational numbers include the integers. 4. Natural numbers: 1,2,3,4, Whole numbers. The numbers 0, 1, 2, 3, …. 6.Integers: …,-3,-2,-1,0,1,2,3,…

2. Vocabulary Continued
7. Nth roots: The number that must be multiplied by itself n times to equal a given value. The nth root can be notated with radicals and indices or with rational exponents, i.e. x1/3 means the cube root of x. 8. Base: The number that is going to be raised to a power. 9. Exponent (power): A number placed above and to the right of another number to show that it has been raised to a power. 10. Index: The number outside the radical symbol. 11. Radicand: is the number found inside a radical symbol, and it is the number you want to find the root of 12. Radical: An expression that uses a root, such as square root, cube root. 13. Rational exponent : For a > 0, and integers m and n, with n > 0, ; am/n = (a1/n)m = (am)1/n .

3. Unit 4: Extending the Number System
Section 1: Review of number systems/ Radicals and rational Exponents

4. How are rational exponents and roots of expressions similar?
Essential Question:
How are rational exponents and roots of expressions similar?

5. Standards In this section- Pages 448-451 in text
Extend the properties of exponents to rational exponents.
MCC9-12.N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents
MCC9-12.N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

6. Number systems review

7. Radicals and Rational Exponents

8. Radical Notation
n is called the index number
a is called the radicand

9. Let’s say you have
63 = 216
this is in exponential notation
put this in radical notation:

10. Properties of Radicals

11. Simplifying Radicals
The radicand has no factor raised to a power greater than or equal to the index number.
2. The radicand has no fractions.
3. No denominator contains a radical.
4. All indicated operations have been performed

12. Simplifying Radicals If there is no index #, it is understood to be 2
Use factor trees to break a number into its prime factors
Apply the properties of radicals and exponents

13. Simplifying Radicals

14. Simplifying radical expressions
Example 1. 2. 3.

15. Examples of simplifying Radical Expressions1. 2.

16. Rational Exponents- When the exponent can be expressed as m/n where m and n are integers and n cannot equal zero
81/3 = = 2
163/4 = =
16 -1/3 =

17. Writing Expressions in radical form
642/3
2. (-8)5/3

18. Writing expressions with rational exponents1. 2.

19. Multiplying Radicals Radicals must have the same index number
Multiply outsides and insides together
Add exponents when multiplying
Simplify your expression
Combine all like terms

20. Assume that all variables represent nonnegative real numbers.

21. Assume that all variables represent nonnegative real numbers.

22. Dividing Radicals No radicals in the denominator
No fractions under the radicand
Apply the properties of radicals and exponents

23. Assume that all variables represent nonnegative real numbers and that no denominators are zero.

24. Assume that all variables represent nonnegative real numbers and that no denominators are zero.

25. Assume that all variables represent nonnegative real numbers and that no denominators are zero.

26. Assume that all variables represent nonnegative real numbers and that no denominators are zero.

27. Simplifying each expression
Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive.

28. Simplifying each expression
Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive.

29. Simplifying each expression
Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive.

30. Homework:
Worksheet 4-1 and 4-2
homework- P 451 # 1-3, 9, 13-19, , 37-40
Coach book: Pages # 1-15