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Lesson Menu Five-Minute Check (over Lesson 10–1) Then/Now New Vocabulary Key Concept: Irrational Number Example 1: Classify Real Numbers Example 2: Compare Real Numbers Example 3: Order Real Numbers Example 4: Solve Equations Example 5: Real-World Example: Use RealExample 5: Real-World Example: Use Real Numbers to Solve ProblemsNumbers to Solve Problems

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Over Lesson 10–1 5-Minute Check 1 A. B. C.6 D.7

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Over Lesson 10–1 5-Minute Check 2 A.9 B.10 C.11 D.12

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Over Lesson 10–1 5-Minute Check 3 A.–9 B.–8 C.7 D.8

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Over Lesson 10–1 5-Minute Check 4 A.7 B.8 C.9 D.10

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Over Lesson 10–1 5-Minute Check 5 A.12 cm B.14 cm C.15 cm D.20 cm The area of a square is 200 cm 2. Estimate the length of a side of the square.

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Over Lesson 10–1 5-Minute Check 6 A.A B.B C.C D.D

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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 irrational numbers real numbers

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Concept

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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 1 CYP A A.rational number B.irrational number C.integer, rational number D.whole number A. Name all the sets of numbers to which the real number 0.380 belongs. Write whole, integer, rational, or irrational.

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Example 1 CYP B A.rational number B.irrational number C.integer, rational number D.whole number B. Name all the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.

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Example 1 CYP C A.rational B.whole, integer, rational C.whole, integer D.irrational C. Name all the sets of numbers to which –2.25 belongs. Write whole, integer, rational, or irrational.

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Example 1 CYP D A.rational B.whole, integer, rational C.whole, integer D.irrational D. Name all the sets of numbers to which belongs. Write whole, integer, rational, or irrational.

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Example 2 Compare Real Numbers Express each number as a decimal. Then compare the decimals.

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Example 2 Compare Real Numbers

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Example 2 CYP A.< B.> C.= D.none of the above

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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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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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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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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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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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