Warm Up Find the two square roots of each number. Evaluate each expression.

1. 3. 8+ 144 4. 7 289 Warm Up Find the two square roots of each number. Evaluate each expression. 1. 144 2. 256 ±12 ±16 20 119 5. A square window has an area of 169 square inches, how wide is the window? 6. A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?

2. 4-6 Learn to estimate square roots to a given number of decimal places and solve problems using square roots. Course 3

3. Estimating Square Roots of Numbers Each square root is between two integers. Name the integers. Explain your answer.

4. 55 is between 7 and 8 because 55 is between 49 and 64. Example 1 Think: What are perfect squares close to 55? 55 49 < 55 72 = 49 64 > 55 82 = 64

5. – is between –9 and –10 because 90 is between 81 and 100. 90 Example 2 Think: What are perfect squares close to 90? – 90 81 < 90 –92 = 81 100 > 90 –102 = 100

6. 80 is between 8 and 9 because 80 is between 64 and 81. Example 3 Think: What are perfect squares close to 80? 80 64 < 80 82 = 64 81 > 80 92 = 81

7. – is between –6 and –7 because 45 is between 36 and 49. 45 Example 4 Think: What are perfect squares close to 45? – 45 36 < 45 –62 = 36 49 > 45 –72 = 49

8. Estimating Large Square Roots Use a calculator to find answer, round to the nearest tenth.

9. Example 5 Use a calculator to find 600. Round to the nearest tenth. Using a calculator, 600 ≈ 24.49489742…. Rounded, 600 is 24.5.

10. Using a calculator, 800 ≈ 28.2842712…. Example 6 Use a calculator to find 800. Round to the nearest tenth. Rounded, 800 is 28.3.

11. Lesson Summary Each square root is between two integers. Name the two integers. 1. 27 2. – 456 5 and 6 –22 and –21 Use a calculator to find each value. Round to the nearest tenth. 9.4 35.0 3. 89 4. 1223 5. A square field has an area of 2000 square feet. To the nearest foot, how much fencing would be needed to enclose the field? 179 ft