64 Chapter 1 Whole Numbers Example 2 19 164 11 10 19 3 1322 3 3 9 164 8 1822 8 8 64 125 1 TIP: To simplify square roots, it is advisable to become familiar with these 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 Skill Practice Find the square roots. 4. 14 5. 1100 6. 1400 7. 1121 Answers 4. 2 5. 10 6. 20 7. 11 2. Square Roots To square a number means that we multiply the base times itself. For example, To find a positive square root of a number means that we reverse the process of squaring. For example, finding the square root of 25 is equivalent to asking, “What positive number, when squared, equals 25?”The symbol (called a radical sign) is used to denote the positive square root of a number. Therefore, is the positive number that, when squared, equals 25. Thus, because Evaluating Square Roots Find the square roots. a. b. c. d. Solution: a. because b. because c. 11 1 because 1122 1 1 1 d. 10 0 because 1022 0 0 0 125 5 1522 25. 52 5 5 25. 3. Order of Operations A numerical expression may contain more than one operation. For example, the following expression contains both multiplication and subtraction. 18 5122 The order in which the multiplication and subtraction are performed will affect the overall outcome. Multiplying first yields Subtracting first yields 18 5122 18 10 18 5122 13122 8 26 (correct) (incorrect) To avoid confusion, mathematicians have outlined the proper order of operations. In particular, multiplication is performed before addition or subtraction.The guidelines for the order of operations are given next. These rules must be followed in all cases.
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