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A#16 / Holt Chapter 1 Ready to Go On? Part 1 Homework Worksheet

This homework and classwork assignment focuses on evaluating expressions containing square roots and classifying numbers within the real number system.

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A#16 / Holt Chapter 1 Ready to Go On? Part 1 Homework Worksheet

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  1. 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)

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

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

  4. 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

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

  6. Reading Math 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. 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!

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

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

  9. 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.

  10. Rational numbers can be expressed in the form , where a and b are both integers and b ≠ 0: , , . 1 2 a b 7 1 9 10 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 numbersare 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, …

  11. Repeating decimalsare 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 Page 18 Terminating decimals are rational numbers in decimal form that have a finite number of digits: 1.5, 2.75, 4.0

  12. 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.

  13. 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

  14. 7 can be written as a repeating decimal. 4 9 A. 7 67  9 = 7.444… = 7.4 49 B. = 3.16227766… Your Turn 2 Page 20 Write all classifications that apply to each real number. rational number (Q), repeating decimal The digits continue with no pattern. irrational number

  15. 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

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

  17. Homework • Assignment #17 • 1-5 Homework Worksheet

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