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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

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

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

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

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

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.

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

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.

Vocabulary irrational numbers real numbers

Concept

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

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.

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:

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:

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 belongs. Write whole, integer, rational, or irrational.

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.

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.

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.

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

Example 2 Compare Real Numbers

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

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

Example 3 Order Real Numbers

Example 3 CYP A. B. C. D.

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

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.

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.

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.

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

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.

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

End of the Lesson