1 5 Square Roots and Real Numbers Homework

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

Warm Up 1 -5 Square Roots and Real Numbers Evaluate each expression. 1. 62 3. (-9) 2. 112 4. Write each fraction as a decimal. 5. 7. Holt Algebra 1 6. 8.

Classwork 1 -5 Square Roots and Real Numbers • Squares Exploration Worksheet Each person will need: - 20 tiles Holt Algebra 1

1 -5 Square Roots and Real Numbers 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 Holt Algebra 1

1 -5 Square Roots and Real Numbers 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. Holt Algebra 1

1 -5 Square Roots and Real Numbers 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 Holt Algebra 1 is not a real number!

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

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

1 -5 Square Roots and Real 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. Holt Algebra 1

1 -5 Square Roots and Real Numbers 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, … Rational numbers can be expressed in the form a , b where a and b are both integers and b ≠ 0: 1, 7, 9. 2 1 10 Holt Algebra 1

1 -5 Square Roots and Real Numbers 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 a form. They include square roots of whole b numbers that are not perfect squares and nonterminating decimals that do not repeat: , , Holt Algebra 1

1 -5 Square Roots and Real Numbers All numbers that can be represented on a Pages 18 – 19 number line are called real numbers and can be classified according to their characteristics. Holt Algebra 1

1 -5 Square Roots and Real Numbers Page 20 Example 2: Classifying Real Numbers Write all classifications that apply to each real number. A. – 32 32 can be written as a fraction and a – 32 = – 32. 0 decimal. 1 rational number (Q), integer (Z), terminating decimal B. 5 5 = 5. 0 1 rational number (Q), (W), natural number 5= Holt Algebra 1 5 can be written as a fraction and a decimal. integer (Z), whole number (N), terminating decimal

1 -5 Square Roots and Real Numbers Page 20 Your Turn 2 Write all classifications that apply to each real number. 4 9 67 9 = 7. 444… = 7. 4 A. 7 4 79 can be written as a repeating decimal. rational number (Q), repeating decimal B. = 3. 16227766… irrational number Holt Algebra 1 The digits continue with no pattern.

Cornell Notes 1 -5 Square Roots and Real Numbers Page 21 • 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. Holt Algebra 1