1. 4-6 Estimating Square Roots Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 4-6 Estimating Square Roots Warm Up Find the two square roots of each number. Evaluate each expression. 1216 20 119 1. 144 2. 256 3. 8+ 144 4. 7 289

3. 4-6 Estimating Square Roots Problem of the Day A pyramid of blocks is built in layers. The bottom layer has 6 2, or 36, blocks. The next layer has 5 2 blocks, and so on until the top layer has 1 block. How many blocks are there in all? 91 blocks

4. 4-6 Estimating Square Roots MA.8.A.6.2 Make reaonable approximations of square roots…,and use them to estimate solutions to problems… Sunshine State Standards

5. 4-6 Estimating Square Roots Additional Example 1A: Estimating Square Roots of Numbers The square root is between two integers. Name the integers. Explain your answer. 55 Think: What are perfect squares close to 55? 7 2 = 49 49 < 55 8 2 = 64 64 > 55 55 is between 7 and 8 because 55 is between 49 and 64.

6. 4-6 Estimating Square Roots 90 – Additional Example 1B: Estimating Square Roots of Numbers Continued Think: What are perfect squares close to 90? –9 2 = 81 81 < 90 –10 2 = 100 100 > 90 The square root is between two integers. Name the integers. Explain your answer. is between –9 and –10 because 90 is between 81 and 100. 90 –

7. 4-6 Estimating Square Roots Check It Out: Example 1A Each square root is between two consecutive integers. Name the integers. Explain your answer. 80 8 2 = 64 and 9 2 = 81; 80 80 is between 64 and 81, so 80 is between 8 and 9.

8. 4-6 Estimating Square Roots Check It Out: Example 1B Each square root is between two consecutive integers. Name the integers. Explain your answer. 105 10 2 = 100 and 11 2 = 121; 105 105 is between 100 and 121, so 105 is between 10 and 11.

9. 4-6 Estimating Square Roots You want to sew a fringe on a square tablecloth with an area of 500 square inches. Calculate the length of each side of the tablecloth and the length of fringe you will need to the nearest inch. Additional Example 2: Application 484 < 500 < 529 List the perfect squares nearest 500. Find the square roots of the perfect squares. The length of each side of the table is about 22 in., and you will need about 88 in. of fringe. The number will be between 22 and 23. The length of each side of the square is √ 500.

10. 4-6 Estimating Square Roots Check It Out: Example 2 You want to build a fence around a square garden that is 250 square feet. Calculate the length of one side of the garden and the total length of the fence, to the nearest tenth. 15 2 = 225 and 16 2 = 256; √250 is much closer to 16. 15.8 2 ≈ 249.64 so ≈ 15.8; side length: 15.8 ft; total length: 63.2 ft √ 250

11. 4-6 Estimating Square Roots Approximate to the nearest hundredth. Additional Example 3: Approximating Square Roots to the Nearest Hundredth 121 < 141 < 144 Find the perfect squares nearest 141. Find the square roots of the perfect squares. The number will be between 11 and 12. The whole number part of the answer is 11. Step 1: Find the value of the whole number.

12. 4-6 Estimating Square Roots Approximate to the nearest hundredth. Additional Example 3 Continued 141 – 121 = 20 Find the difference between the given number, 141, and the lower perfect square. Find the difference between the greater perfect square and the lower perfect square. Write the difference as a ratio. 20  23 ≈ 0.869 Step 2: Find the value of the decimal. 144 – 121 = 23 20 23 Divide to find the approximate decimal value.

13. 4-6 Estimating Square Roots 11 + 0.869 = 11.869 Combine the whole number and decimal. Round to the nearest hundredth. Step 3: Find the approximate value. 11.869 ≈ 11.87 Approximate to the nearest hundredth. Additional Example 3 Continued The approximate value of to the nearest hundredth is 11.87.

14. 4-6 Estimating Square Roots Estimate 154 to the nearest hundredth. Check It Out: Example 3 144 < 154 < 169; 154 – 144 169 – 144 = 10 25 = 0.4; 154 ≈ 12.40

15. 4-6 Estimating Square Roots Additional Example 4: Using a Calculator to Estimate the Value of a Square Root Using a calculator, 600 ≈ 24.49489742 …. Rounded, 600 is 24.5. Use a calculator to find 600. Round to the nearest tenth.

16. 4-6 Estimating Square Roots Check It Out: Example 4 800 = 28.28427125 ≈ 28.3 Use a calculator to find 800. Round to the nearest tenth.

17. 4-6 Estimating Square Roots Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

18. 4-6 Estimating Square Roots Lesson Quiz Each square root is between two integers. Name the two integers. 1. 27 2. – 456 Use a calculator to find each value. Round to the nearest tenth. 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? 5 and 6–22 and –21 9.435.0 179 ft

19. 4-6 Estimating Square Roots 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 Lesson Quiz for Student Response Systems

20. 4-6 Estimating Square Roots 2. Use a calculator to round to the nearest tenth. A. 2.3 B. 4.5 C. 6.7 D. 9.2 Lesson Quiz for Student Response Systems

21. 4-6 Estimating Square Roots 3. Name the two integers the square root is between. A. –2 and –3 B. –10 and –11 C. –14 and –15 D. –15 and –16 Lesson Quiz for Student Response Systems