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Over Lesson 10–1 A.A B.B C.C D.D 5-Minute Check 4 The area of a square is 200 cm 2. Estimate the length of a side of the square.

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Splash Screen

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Then/Now You have already compared fractions and decimals. (Lesson 3–1) Identify and compare numbers in the real number system. Solve equations by finding square roots.

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Vocabulary A long time ago in a galaxy far, far away…wrong slide show (just a long time ago, someone created numbers) Natural Number (Counting Numbers) – 1,2,3,… Whole Numbers – 0,1,2,3,… Integers – …-3,-2,-1,0,1,2,3,… Rational Numbers – numbers that can be fractions (⅓,.375, etc) Irrational Numbers – numbers that cannot be fractions (, π, etc) Real Numbers – both Rational and Irrational Numbers

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Real Number Rational Numbers Irrational Numbers Whole Numbers Natural Numbers Integers

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Example 1 A Classify Real Numbers A. Name all of the sets of numbers to which the real number 0.246 belongs. Write whole, integer, rational, or irrational. Answer: This decimal is a rational number because its digits repeat. It is equivalent to

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Example 1 B Classify Real Numbers Answer: Since this number is a whole number, an integer, and a rational number. B. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.

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Example 1 C Classify Real Numbers C. Name all the sets of numbers to which the real number –7.25 belongs. Write whole, integer, rational, or irrational. Answer:

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Example 1 D Classify Real Numbers D. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational. Answer:

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Example 3 Order Real Numbers Express each number as a decimal. Then order the decimals.

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Example 3 Order Real Numbers

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A.A B.B C.C D.D Example 3 CYP A. B. C. D.

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Example 4 A Solve Equations A. Solve w 2 = 169. Round to the nearest tenth, if necessary. w 2 =169Write the equation. Answer: The solutions are 13 and –13. Definition of square root. w=13 or w = –13

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Example 4 Solve Equations B. Solve r 2 = 50. Round to the nearest tenth, if necessary. r 2 =50Write the equation. Answer: The solutions are approximately 7.1 and –7.1. Definition of square root. Use a calculator.

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A.A B.B C.C D.D Example 4 CYP A A.8 B.8 and –8 C.9 D.9 and –9 A. Solve the equation m 2 = 81. Round to the nearest tenth, if necessary.

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A.A B.B C.C D.D Example 4 CYP B A.4.8 and –4.8 B.4.9 C.4.9 and –4.9 D.5 and –5 B. Solve the equation h 2 = 24. Round to the nearest tenth, if necessary.

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Example 5 Use Real Numbers to Solve Problems Write the formula. Replace R with 6.4 and A with 40.

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Example 5 Use Real Numbers to Solve Problems Answer: The wingspan is 16 feet. Multiply each side by 40. Consider only the positive square root. Simplify.

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A.A B.B C.C D.D Example 5 A.7.1 ft B.9.9 ft C.14 ft D.98 ft

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End of the Lesson

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