Splash Screen.

Slides:

Advertisements

Similar presentations

Square Roots/Rational Numbers

Advertisements

Warm Up Simplify each expression

Square Roots and Real Numbers

7N1 PLUS The Real Number System (rational and irrational)

Lesson Menu Main Idea and New Vocabulary Key Concept:Pythagorean Theorem Example 1:Find a Missing Length Example 2:Find a Missing Length Key Concept:Converse.

Square Roots and Real Numbers

Holt Algebra Square Roots and Real Numbers 1-5 Square Roots and Real Numbers Holt Algebra 1 Lesson Presentation Lesson Presentation Lesson Quiz Lesson.

The Real Number System. Real Numbers The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all.

Over Chapter 9 A.A B.B C.C D.D 5-Minute Check 1 A.10a 2 b 3 B.5 2 a 2 b 3 C.10ab 5 D.5ab 5 Write 5 ● 5 ● a ● a ● b ● b ● b using exponents.

Lesson 9-2 Pages The Real Number System Lesson Check 9-1.

Over Lesson 11–7 A.A B.B C.C D.D 5-Minute Check 1 Find the circumference of the circle to the nearest tenth.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–1) Then/Now New Vocabulary Key Concept: Irrational Number Example 1: Classify Real Numbers.

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.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 11–7) Then/Now New Vocabulary Key Concept: Area of a Circle Example 1: Find Areas of Circles.

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.

Transparency 3 Click the mouse button or press the Space Bar to display the answers.

Lesson 3-3 The Real Number System.

Warm Up Find each quotient / divided by 3/5

Splash Screen. Then/Now You solved quadratic equations by completing the square. Solve quadratic equations by using the Quadratic Formula. Use the discriminant.

Lesson 4 Contents 11-3 Solving Quadratic Equations by Using the Quadratic Formula Objectives 1. Solve quadratic equations by using the Quadratic Formula.

3-6 Estimating Square Roots Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

1-2 Irrational Numbers and Square Roots. Geogebra Finding square roots of perfect squares Estimating a square root Comparing square roots Surface area.

1-2 Irrational Numbers and Square Roots. Video Tutor Help Irrational Numbers Classifying Real Numbers Khan Academy Word Problem: given area find side.

The Real Numbers 3-7 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

Splash Screen Unit 6 Exponents and Radicals. Splash Screen Essential Question: How do you evaluate expressions involving rational exponents?

Bell Work: Simplify.√8 3. Answer:2 Lesson 16: Irrational Numbers.

Main Idea and New Vocabulary Key Concept: Pythagorean Theorem

Estimating Square Roots

Estimating Square Roots

Write each fraction as a decimal.

A B C D Solve x2 + 8x + 16 = 16 by completing the square. –8, 0

Five-Minute Check (over Lesson 3–4) Mathematical Practices Then/Now

Exploring Square Roots and Irrational Numbers

Square Roots and Real Numbers

Write each fraction as a decimal.

Objectives Evaluate expressions containing square roots.

Square Roots and Real Numbers

Square Roots and Real Numbers

Five-Minute Check (over Lesson 12–3) Then/Now

You have already compared fractions and decimals. (Lesson 3–1)

Main Idea and New Vocabulary Key Concept: Pythagorean Theorem

Main Idea and New Vocabulary Key Concept: Area of a Circle

Square Roots and Real Numbers

Warm Up Simplify each expression

Square Roots and Real Numbers

Write each fraction as a decimal.

Presentation transcript:

Splash Screen

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 Real Numbers to Solve Problems Lesson Menu

A. B. C. 6 D. 7 5-Minute Check 1

A. 9 B. 10 C. 11 D. 12 5-Minute Check 2

A. –9 B. –8 C. 7 D. 8 5-Minute Check 3

A. 7 B. 8 C. 9 D. 10 5-Minute Check 4

The area of a square is 200 cm2 The area of a square is 200 cm2. Estimate the length of a side of the square. A. 12 cm B. 14 cm C. 15 cm D. 20 cm 5-Minute Check 5

A. A B. B C. C D. D 5-Minute Check 6

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. Then/Now

irrational numbers real numbers Vocabulary

Concept

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 Example 1 A

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

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 C

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 D

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. A. rational number B. irrational number C. integer, rational number D. whole number Example 1 CYP A

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. A. rational number B. irrational number C. integer, rational number D. whole number Example 1 CYP B

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. A. rational B. whole, integer, rational C. whole, integer D. irrational Example 1 CYP C

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. A. rational B. whole, integer, rational C. whole, integer D. irrational Example 1 CYP D

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

Compare Real Numbers Example 2

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

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

Order Real Numbers Example 3

A. B. C. D. Example 3 CYP

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

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

A. Solve the equation m2 = 81. Round to the nearest tenth, if necessary. B. 8 and –8 C. 9 D. 9 and –9 Example 4 CYP A

B. Solve the equation h2 = 24. Round to the nearest tenth, if necessary. A. 4.8 and –4.8 B. 4.9 C. 4.9 and –4.9 D. 5 and –5 Example 4 CYP B

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

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

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

End of the Lesson