60 Chapter 1 The Set of Real Numbers Example 2 19 3 1322 9. 164 8 1822 64 1121 11 11122 121 10 0 1022 0 2 3 4 9 2 3 TIP: To simplify square roots, it is advisable to become familiar with these perfect squares and square roots. 02 0 10 0 72 49 149 7 12 1 11 1 82 64 164 8 22 4 14 2 92 81 181 9 32 9 19 3 102 100 1100 10 42 16 116 4 112 121 1121 11 52 25 125 5 122 144 1144 12 62 36 136 6 132 169 1169 13 181 1100 Classroom Examples: p. 67, Exercises 36 and 44 Answers 5. 9 6. 10 7. 1 8. 3 5 2. Square Roots If we reverse the process of squaring a number, we can find the square roots of the number. For example, finding a square root of 9 is equivalent to asking “what number(s) when squared equals 9?” The symbol, (called a radical sign), is used to find the principal square root of a number. By definition, the principal square root of a number is nonnegative. Therefore, is the nonnegative number that when squared equals 9. Hence because 3 is nonnegative and Evaluating Square Roots Evaluate the square roots. a. b. c. d. Solution: a. Because b. Because c. Because d. Because A perfect square is a number whose square root is a rational number. If a number is not a perfect square, its square root is an irrational number that can be approximated on a calculator. 2 3 4 B 9 B 4 9 164 1121 10 19 1 Skill Practice Evaluate. 5. 6. 7. 8. B 9 25 11 3. Order of Operations When algebraic expressions contain numerous operations, it is important to evaluate the operations in the proper order. Parentheses brackets and braces are used for grouping numbers and algebraic expressions. It is important 5 6 1 2, 3 4, to recognize that operations must be done within parentheses and other grouping symbols first. Other grouping symbols include absolute value bars, radical signs, and fraction bars.
miller_introductory_algebra_3e_ch1_3
To see the actual publication please follow the link above