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,... 5. Whole numbers. The numbers 0, 1, 2, 3, …. 6.Integers: …,-3,-2,-1,0,1,2,3,…

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 .

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

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

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.

Number systems review

Radicals and Rational Exponents

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

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

Properties of Radicals

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

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

Simplifying Radicals

Simplifying radical expressions Example 1. 2. 3.

Examples of simplifying Radical Expressions 1. 2.

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 =

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

Writing expressions with rational exponents 1. 2.

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

Assume that all variables represent nonnegative real numbers.

Assume that all variables represent nonnegative real numbers.

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

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

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

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

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

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

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

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

Homework: Worksheet 4-1 and 4-2 homework- P 451 # 1-3, 9, 13-19, 25- 28, 37-40   Coach book: Pages 174-175 # 1-15