1. Lesson 3-2 Ideas/Vocabulary Estimate square roots.

2. Lesson 3-2 TEKS 8.1 The student understands that different forms of numbers are appropriate for different situations. (C) Approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as π, ).

3. Lesson 3-2 Example 1 Estimate Square Roots The first perfect square greater than 54 is 64. The first perfect square less than 54 is 49. Estimate to the nearest whole number. Plot each square root on a number line. Then plot.

4. Lesson 3-2 Example 1 Estimate Square Roots 49 < 54 < 64Write an inequality. 7 2 < 54 < 8 2 49 = 7 2 and 64 = 8 2 Find the square root of each number. 7 < < 8Simplify. Answer: So, is between 7 and 8. Since 54 is closer to 49 than 64, the best whole number estimate for is 7.

5. A. A B. B C. C D. D Lesson 3-2 Example 1 CYP A.5 B.6 C.7 D.8 Estimate to the nearest whole number.

6. Lesson 3-2 Example 2 Estimate Square Roots The first perfect square greater than 41.3 is 49. The first perfect square less than 41.3 is 36. Estimate to the nearest whole number. Plot each square root on a number line. Then plot

7. 6 < < 7Simplify. Find the square root of each number. Lesson 3-2 Example 2 Estimate Square Roots 36 < 41.3 < 49Write an inequality. 6 2 < 41.3 < 7 2 36 = 6 2 and 49 = 7 2 Answer: So, is between 6 and 7. Since 41.3 is closer to 36 than 49, the best whole number estimate for is 6.

8. Estimate to the nearest whole number. A. A B. B C. C D. D Lesson 3-2 Example 2 CYP A.3 B.4 C.5 D.6

9. Lesson 3-2 Example 3 FINANCE If you were to invest $100 in a bank account for two years, your investment would earn interest daily and be worth more when you withdrew it. If you had $120 after two years, the interest rate, written as a decimal, would be found using the expression. Estimate this value. Estimate Square Roots to Solve a Problem

10. Lesson 3-2 Example 3 100 < 120 < 121100 and 121 are the closest perfect squares. 10 2 < 120 < 11 2 100 = 10 2 and 121 = 11 2 10 < < 11Find the square root of each number. First estimate the value of Estimate Square Roots to Solve a Problem

11. Lesson 3-2 Example 3 Answer: The approximate interest rate is 0.10 or 10%. Since 120 is closer to 121 than 100, the best whole number estimate for is 11. Use this to evaluate the expression. Estimate Square Roots to Solve a Problem

12. Lesson 3-2 Example 3 CYP FINANCE If you were to invest $100 in a bank account for two years, your investment would earn interest daily and be worth more when you withdrew it. If you had $150 after two years, the interest rate, written as a decimal, would be found using the expression. Estimate this value.

13. A. A B. B C. C D. D Lesson 3-2 Example 3 CYP A.0.10 B.0.15 C.0.20 D.0.25 FINANCE Estimate the value of.