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Name Class Date Lesson 1-2 Irrational Numbers and Square Roots Lesson Objective Common Core Standards To find and estimate square roots and to classify numbers as rational or irrational The Number System: 8.NS.1, 8.NS.2 Expressions and Equations: 8.EE.2 Vocabulary The square root of a number is a number that when multiplied by itself is equal to the given number. a b numbers that cannot be written in the form , where a is Irrational numbers are any integer and b is any nonzero integer. All rights reserved. A perfect square is a number that is the square of a whole number. set of rational and irrational numbers. The real numbers are the Examples a. 81 b. 9 9 5 81 and 29 29 5 81 The two square roots of 81 are 9 and 29 . 1 36 1 1 1 1 5 and 2 6 6 6 36 The two square roots of 2 Estimating a Square Root Estimate the value 81 of 2 70 to the nearest integer and to the nearest tenth. 1 26 5 1 are 1 and 1 · 6 6 36 Since 70 is closer to 70.56 than to 68.89, 2 70 ¯ 28.4 . 64 70 8 9 Since 70 is closer to 64 than it is to 81, 2 70 ¯ 28 . 1 36 70 70.56 68.89 83 84 Quick Check 1. Find the square roots of each number. a. 36 b. 1 6, 26 1, 21 c. 1 16 © Pearson Education, Inc., publishing as Pearson Prentice Hall. 1 Finding Square Roots of Perfect Squares Find the two square roots of each number. 1, 1 24 4 2. Estimate the value of 38 to the nearest integer and to the nearest tenth. 6; 6.2 4 441198_C3_Ch1_WKbk_Ver-1.indd 4 Course 3 Lesson 1-2 Daily Notetaking Guide 10/10/12 4:19 PM Name Class Date Examples 3 Comparing Square Roots Which is greater, 28 or 5.1? First, estimate the value of the square root to the nearest tenth. 28 ¯ 5.3 Since 5.3 . 5.1, 28 . 5.1. 4 Surface Area of a Sphere The formula S.A. 5 13r2 gives the approximate All rights reserved. surface area S.A. in square units of a sphere with radius r. Find the radius of a sphere with surface area 650 square units. S.A. 5 13r2 ← Use the formula for the surface area of a sphere. 650 5 13r2 ← Substitute 650 650 5 r2 13 50 ¯ r2 50 ¯ for S.A. ← Divide each side by 13 to isolate r. ← Simplify. r 2 ← Find the positive square root of each side. Use a calculator. 7.1 ¯ r ← Round to the nearest tenth. The radius of a sphere with surface area 650 square units is about 7.1 units. 5 Classifying Real Numbers Is each number rational or irrational? © Pearson Education, Inc., publishing as Pearson Prentice Hall. Explain. a. 29333.3 b. 4 c. 7 9 Rational ; the decimal repeats. Rational ; the number can be written as the ratio Irrational ; 90 is not a 90 Irrational d. 6.363663666 . . . perfect 43 . 9 square. ; the decimal does not terminate or repeat. Quick Check 3. Which is greater 20 or 4.7? 4.7 4. Use the formula S.A. 5 13r2 to find the radius of a sphere with a surface area of 520 square units. Round to the nearest tenth of a unit. 6.3 units _ 5. Is 0.6 rational or irrational? Explain. Rational; the decimal repeats. Daily Notetaking Guide 441198_C3_Ch1_WKbk_Ver-1.indd 5 Course 3 Lesson 1-2 5 10/10/12 4:19 PM