Learn to estimate square roots and solve problems using square roots. 1

Example 1: Estimating Square Roots of Numbers The square root is between two integers. Name the integers. Explain your answer. Think: What are perfect squares close to 55? 55 72 = 49 49 < 55 82 = 64 64 > 55 55 is between 7 and 8 because 55 is between 49 and 64. 2

Example 2: Estimating Square Roots of Numbers Continued The square root is between two integers. Name the integers. Explain your answer. Think: What are perfect squares close to 90? – 90 –92 = 81 81 < 90 –102 = 100 100 > 90 is between –9 and –10 because 90 is between 81 and 100. 90 – 3

Think: What are perfect squares close to 80? 80 Example 3 The square root is between two integers. Name the integers. Explain your answer. Think: What are perfect squares close to 80? 80 82 = 64 64 < 80 92 = 81 81 > 80 80 is between 8 and 9 because 80 is between 64 and 81. 4

The square root is between two integers. Name the integers. Example 4 The square root is between two integers. Name the integers. Think: What are perfect squares close to 45? – 45 –62 = 36 36 < 45 –72 = 49 49 > 45 is between –6 and –7 because 45 is between 36 and 49. 45 – 5

Example 5 Approximate to the nearest hundredth. 11.869 11.869 ≈ 11.87 Round to the nearest hundredth. The approximate value of to the nearest hundredth is 11.87.

Example 6 Approximate to the nearest hundredth. 15.484 15.484 ≈ 15.48 Round to the nearest hundredth. The approximate value of to the nearest hundredth is 15.48.

Example 7: Using a Calculator to Estimate the Value of a Square Root Use a calculator to find 600. Round to the nearest tenth. Using a calculator, 600 ≈ 24.49489742…. Rounded, 600 is 24.5. 8

Use a calculator to find 800. Round to the nearest tenth. Example 8 Use a calculator to find 800. Round to the nearest tenth. Using a calculator, 800 ≈ 28.2842712…. Rounded, 800 is 28.3. 9

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 10

Each square root is between two integers. Name the two integers. Lesson Quiz 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. 3. 89 4. 1223 9.4 35.0 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 11

Lesson Quiz for Student Response Systems 1. Name the two integers the square root is between. A. 5 and 6 B. 6 and 7 C. 8 and 9 D. 38 and 40 12

Lesson Quiz for Student Response Systems 2. Use a calculator to round to the nearest tenth. A. 2.3 B. 4.5 C. 6.7 D. 9.2 13 13

Lesson Quiz for Student Response Systems 3. Name the two integers the square root is between. A. –2 and –3 B. –10 and –11 C. –15 and –14 D. –15 and –16 14 14