1. 1-2 Irrational Numbers and Square Roots

2. Video Tutor Help Irrational Numbers Classifying Real Numbers Khan Academy Word Problem: given area find side length Word problem: square roots Estimating square roots Classifying real numbers as rational or irrationalClassifying real numbers as rational or irrational (1-1 and 1-2) Simplifying square rootsSimplifying square roots (1-2) Irrational Numbers and Square Roots Course 3 Rational Exponents Exponents can not only be integers and unit fractions. An exponent can be any rational number expressed as the quotient of two integers. Irrational Numbers and Square Roots Course 3 Simplifying Radical Expressions Radical expressions can often be simplified by moving factors which are perfect roots out from under the radical sign. 1-2 Irrational Numbers and Square Roots Course 3 Irrational Numbers Although the Greeks initially thought all numeric qualities could be represented by the ratio of two integers, i.e. rational numbers, we now know that not all numbers are rational. How do we know this? Irrational Numbers and Square Roots Course 3 Real Numbers There are an infinite number of rational numbers, but there are infinitely more irrational numbers. Neither type of number can represent every type of numeric quantity. By combining the rational and irrational numbers into the real numbers, a continuum of numbers is created which can represent any quantity in the real

3. Simplifying square roots Classifying real numbers as rational or irrational Video Tutor Help

4. Worksheets 1-2 Note-Taking Guide 1-2 Practice 1-2 Guided Problem Solving

5. Vocabulary Practice Chapter 1 Vocabulary (Electronic) Flash Cards

6. Additional Lesson Examples 1-2 Step-by-Step Examples

7. Lesson Readiness 1-2 Problem of the Day 1-2 Lesson Quiz

8. Equivalent Forms of Rational Numbers Write each as a fraction in simplest form. 1. 2. – 3. Write as a decimal. Write each decimal as a mixed number or fraction in simplest form. 4. 2.75 5. 0.4 5757 LESSON 1-1 30 42 2323 – 3434 2 12 18 2 16 0.125 2525 Lesson Quiz

13. Find the two square roots of 81. Exploring Square Roots and Irrational Numbers LESSON 1-2 9 9 = 81 –9 (–9) = 81 The two square roots of 81 are 9 and –9. Additional Examples

14. Example 1-1a Find indicates the positive square root of 81. Since Answer: Find a Square Root

15. Example 1-1b Answer: 8 Find

16. Example 1-2a Find indicates the negative square root of 144. Answer: Since Find the Negative Square Root

17. Example 1-2b Find Answer: ─ 6

19. Estimate the value of – 70 to the nearest integer. Exploring Square Roots and Irrational Numbers LESSON 1-2 Since 70 is closer to 64 than it is to 81, – 70 –8. Additional Examples

21. Math fact: The sum of any number of consecutive odd whole numbers, beginning with 1, is a perfect square e.g. 1+3=4, 1+3+5=9, 1+3+5+7=16

22. Example 1: Estimating Square Roots of Numbers The 55 is between two integers. Name the integers. Explain your answer. List perfect squares near 55.36, 49, 64, 81 49 < 55 < 64 Find the square roots of the perfect squares. 55 55 is between 7 and 8 because 55 is between 49 and 64. Find the perfect squares nearest 55. 49 < 55 < 64 7 < 55 < 8

23. Example 2: Approximating Square Roots to the Nearest Hundredth 121 < 135 < 144 The whole number part of the answer is 11. Find the perfect squares nearest 135. Find the square roots of the perfect squares. √121 < √135 < 144 √ 11 < 135< 12 √ Step 1 Find the value of the whole number. The number will be between 11 and 12. Approximate √135 to the nearest hundredth.

24. Example 2 Continued 135 – 121 = 14 14 ÷ 23 ≈ 0.609 Find the difference between the given number, 135, and the lower perfect square. Approximate √135 to the nearest hundredth. Step 2 Find the value of the decimal. Write the difference as a ratio. 144 – 121 = 23 Find the difference between the greater perfect square and the lower perfect square. 14 23 Divide to find the approximate decimal value.

25. Example 2 Continued 11 + 0.609 = 11.609 Combine the whole number and decimal. Step 3 Find the approximate value. 11.609 ≈ 11.61 Round to the nearest hundredth. The approximate value of 135 to the nearest hundredth is 11.61. Approximate √135 to the nearest hundredth.

26. Example 3: Using a Calculator to Estimate the Value of a Square Root Use a calculator to find 600. Round to the nearest tenth. 600 ≈ 24.5 600 ≈ 24.494897… Use a calculator. Round to the nearest tenth. 600 rounded to the nearest tenth is 24.5.

28. The math class drops a small ball from the top of a stairwell. They measure the distance to the basement as 48 feet. Use the formula d = 16t 2 to find how long it takes the ball to fall. Exploring Square Roots and Irrational Numbers LESSON 1-2 48 = 16t 2 Substitute 48 for d. d = 16t 2 Use the formula. = t 2 Divide each side by 16. 48 16 3 = t 2 Simplify. Additional Examples

29. (continued) Exploring Square Roots and Irrational Numbers LESSON 1-2 It takes about 1.7 seconds for the ball to fall 48 ft. 3 = tFind the positive square root. Use a calculator. 31.7320508 Round to the nearest tenth. 1.7 t Additional Examples

30. Identify each number as rational or irrational. Explain. Exploring Square Roots and Irrational Numbers LESSON 1-2 d. 6.36366366636666... Irrational; the decimal does not terminate or repeat. Rational; the decimal repeats.a. –9.3333 b. 4 7979 Rational; the number can be written as the ratio. 43 9 Irrational; 90 is not a perfect square. c. 90 Additional Examples

31. Example 1-3a ALGEBRA Solve Write the equation. Take the square root of each side. The equation has two solutions, Answer: Notice that Use Square Roots to Solve an Equation

32. Example 1-3b Answer: ALGEBRA Solve

36. Turn and talk