36 Chapter 1 The Set of Real Numbers 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, 19 is the nonnegative number that when squared equals 9. Hence, because 3 is nonnegative and 19 3 1322 9. Evaluating Square Roots Example 2 Evaluate the square roots. a. b. c. d. Solution: a. Because b. Because c. Because 164 8 1822 64 1121 11 11122 121 10 0 1022 0 4 9 2 3 d. Because 2 3 2 3 4 B 9 Skill Practice Evaluate. 5. 6. 7. 8. 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. B 9 25 181 1100 11 B 4 9 164 1121 10 1 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 3. Order of Operations When algebraic expressions contain numerous operations, it is important to evaluate the operations in the proper order. Parentheses 1 2, brackets 3 4, and braces 5 6 are used for grouping numbers and algebraic expressions. It is important Answers 5. 9 6. 10 7. 1 8. 3 5 TIP: To simplify square roots, it is advisable to become familiar with the following perfect squares and square roots. 62 36 136 6 132 169 1169 13
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