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2.7 Find Square Roots and Compare Real Numbers Goal • Find square roots and compare real numbers. Warm-up: Record the definition and show an example for each of the following vocabulary words: square root radical radicand perfect square SQUARE ROOT OF A NUMBER Words If b 2 = a, then ____ is a square root of ____. Numbers 52 = 25 and (−5)2 = 25, so ____ and ____ are square roots of 25. Example 1-Find square roots Evaluate the expression. a. − 36 = ____ The negative square root of 36 is ________. All positive real numbers have two square roots, a positive and a negative square root. The positive square root is called the principal square root. b. 16 = ____ c. ± 64 = ____ The positive square root of 16 is ____. The positive and negative square roots of 64 are ____ and ____. Now YOU try it. Evaluate the expression. 1. 100 Page 3. ± 256 1 2. − 1 Example 2 - Approximate a square root. The top of a folding table is a square whose area is 945 square inches. Approximate the side length of the tabletop to the nearest inch. This means that s is the positive square root of 945. You can use a table determine if 945 is a perfect square. Number Square of a Number As shown in the table, 945 is _______________________________________. The greatest perfect square less than 945 is ________. The least perfect square greater than 945 is _________. The side length of the tabletop is about _____ inches. Now YOU try it. 4. 32 5. 103 Approximate the square root to the nearest integer: 6. - 48 Example 3: Classify numbers Tell whether each of the following numbers is a real number, a rational number, an irrational number, an integer, or a whole number: Number Real Number? Rational Number? 144 , − 49, 32. Irrational Number? Integer? Whole Number? 144 − 49 32 Example 4 - Graph and order real numbers Order the numbers from least to greatest: 4 Graph the numbers on a number line using approximation. , − 5, 13, −2.5, 9 3 Page 2 Read the numbers from left to right: Now YOU try it. 7. Tell whether each of the following numbers is a real number, rational number, irrational number, integer, or whole number and order the numbers from least to greatest by putting them on the number line. Number Real number? Rational number? Irrational number? Integer? Whole number? − 20 − 9 2 0 7 4.1 Page 3 5.2