A#16 / Holt Chapter 1 Ready to Go On? Part 1 Homework Worksheet Homework Corrections A#16 / Holt Chapter 1 Ready to Go On? Part 1 Homework Worksheet 90 – m 2. a) 3 b) 1 3. a) 66 b) 7 4. a) b) undefined 5. a) - 3 ● 3 = -9 b)

Warm Up Evaluate each expression. 1. 62 2. 112 3. (-9)(-9) 4. 1. 62 2. 112 3. (-9)(-9) 4. Write each fraction as a decimal. 5. 6. 8.

Classwork Squares Exploration Worksheet Each person will need: - 20 tiles

Lesson Objectives: I will be able to … Page 18 Lesson Objectives: I will be able to … Evaluate expressions containing square roots Classify numbers within the real number system Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

Page 18 A number that is multiplied by itself to form a product is called a square root of that product. 4 is the square root of 16. 16 is a perfect square of since its square root (4) is a whole number. A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table.

The expression does not represent a real number because there is no real number that can be multiplied by itself to form a product of –36. Reading Math 6 ● 6 = 36 ≠ -36 -6 ● -6 = 36 ≠ -36 6 ● -6 = -36 (but 6 and -6 are not the same number) So is not a real number!

Example 1: Finding Square Roots of Perfect Squares Page 19 Find each square root. A. 42 = 16 Think: What number squared equals 16? = 4 Positive square root positive 4. B. 32 = 9 Think: What is the opposite of the square root of 9? = –3 Negative square root negative 3. C. Think: What number squared equals ? 25 81 Positive square root positive . 5 9

Think: What number squared equals 4? Your Turn 1 Page 19 Find each square root. A. 22 = 4 Think: What number squared equals 4? = 2 Positive square root positive 2. B. 52 = 25 Think: What is the opposite of the square root of 25? Negative square root negative 5.

The square roots of many numbers like , are not whole numbers The square roots of many numbers like , are not whole numbers. A calculator can approximate the value of as 3.872983346... Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers.

Natural numbers are the counting numbers: 1, 2, 3, … Page 18 All numbers that can be represented on a number line are called real numbers and can be classified according to their characteristics. Natural numbers are the counting numbers: 1, 2, 3, … Whole numbers are the natural numbers and zero: 0, 1, 2, 3, … Integers are whole numbers and their opposites: –3, –2, –1, 0, 1, 2, 3, … a b Rational numbers can be expressed in the form , where a and b are both integers and b ≠ 0: , , . 1 2 7 9 10

Terminating decimals are rational numbers in Page 18 Terminating decimals are rational numbers in decimal form that have a finite number of digits: 1.5, 2.75, 4.0 Repeating decimals are rational numbers in decimal form that have a block of one or more digits that repeat continuously: 1.3, 0.6, 2.14 Irrational numbers cannot be expressed in the form . They include square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat: , ,  a b

and can be classified according to their characteristics. All numbers that can be represented on a number line are called real numbers Pages 18 – 19 and can be classified according to their characteristics.

Example 2: Classifying Real Numbers Page 20 Write all classifications that apply to each real number. A. –32 32 1 32 can be written as a fraction and a decimal. –32 = – = –32.0 rational number (Q), integer (Z), terminating decimal B. 5 5 1 5 can be written as a fraction and a decimal. 5 = = 5.0 rational number (Q), integer (Z), whole number (W), natural number (N), terminating decimal

Write all classifications that apply to each real number. Your Turn 2 Page 20 Write all classifications that apply to each real number. A. 7 4 9 7 can be written as a repeating decimal. 49 67  9 = 7.444… = 7.4 rational number (Q), repeating decimal B. The digits continue with no pattern. = 3.16227766… irrational number

Cornell Notes Fill in the Essential Question: “How do I evaluate expressions containing square roots and classify numbers?” Write two or three main ideas from this lesson in the Notes section. Write a Question for each main idea. (The answer to the question should be the main idea.) Summarize the answers to your questions in the Summary section. Page 21

Classwork Am I Rational ? Each person will need: - white board - dry erase marker

Homework Assignment #17 1-5 Homework Worksheet