4 6 Estimating Square Roots Warm Up Problem

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

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

4 -6 Estimating Square Roots Problem of the Day A pyramid of blocks is built in layers. The bottom layer has 62, or 36, blocks. The next layer has 52 blocks, and so on until the top layer has 1 block. How many blocks are there in all? 91 blocks

4 -6 Estimating Square Roots Sunshine State Standards MA. 8. A. 6. 2 Make reaonable approximations of square roots…, and use them to estimate solutions to problems…

4 -6 Estimating Square Roots Additional Example 1 A: 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? 72 = 49 49 < 55 82 = 64 64 > 55 55 is between 7 and 8 because 55 is between 49 and 64.

4 -6 Estimating Square Roots Additional Example 1 B: Estimating Square Roots of Numbers Continued The square root is between two integers. Name the integers. Explain your answer. Think: What are perfect – 90 squares close to 90? – 92 = 81 81 < 90 – 102 = 100 > 90 – 90 is between – 9 and – 10 because 90 is between 81 and 100.

4 -6 Estimating Square Roots Check It Out: Example 1 A Each square root is between two consecutive integers. Name the integers. Explain your answer. 80 80 82 = 64 and 92 = 81; 80 is between 64 and 81, so and 9. 80 is between 8

4 -6 Estimating Square Roots Check It Out: Example 1 B Each square root is between two consecutive integers. Name the integers. Explain your answer. 105 102 = 100 and 112 = 121; 105 is between 100 and 121, so between 10 and 11. 105 is

4 -6 Estimating Square Roots Additional Example 2: Application 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. The length of each side of the square is √ 500. 484 < 500 < 529 List the perfect squares nearest 500. Find the square roots of the perfect squares. The number will be between 22 and 23. The length of each side of the table is about 22 in. , and you will need about 88 in. of fringe.

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. 152 = 225 and 162 = 256; √ 250 is much closer to 16. 15. 82 ≈ 249. 64 so √ 250 ≈ 15. 8; side length: 15. 8 ft; total length: 63. 2 ft

4 -6 Estimating Square Roots Additional Example 3: Approximating Square Roots to the Nearest Hundredth Approximate to the nearest hundredth. Step 1: Find the value of the whole number. 121 < 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.

4 -6 Estimating Square Roots Additional Example 3 Continued Approximate to the nearest hundredth. Step 2: Find the value of the decimal. Find the difference between the given 141 – 121 = 20 number, 141, and the lower perfect square. Find the difference between the 144 – 121 = 23 greater perfect square and the lower perfect square. 20 Write the difference as a ratio. 23 Divide to find the approximate 20 23 ≈ 0. 869 decimal value.

4 -6 Estimating Square Roots Additional Example 3 Continued Approximate to the nearest hundredth. Step 3: Find the approximate value. 11 + 0. 869 = 11. 869 ≈ 11. 87 Combine the whole number and decimal. Round to the nearest hundredth. The approximate value of hundredth is 11. 87. to the nearest

4 -6 Estimating Square Roots Check It Out: Example 3 Estimate 154 to the nearest hundredth. 144 < 154 < 169; 154 – 144 = 10 169 – 144 25 = 0. 4; 154 ≈ 12. 40

4 -6 Estimating Square Roots Additional Example 4: Using a Calculator to Estimate the Value of a Square Root Use a calculator to find the nearest tenth. Using a calculator, Rounded, 600. Round to 600 ≈ 24. 49489742…. 600 is 24. 5.

4 -6 Estimating Square Roots Check It Out: Example 4 Use a calculator to find the nearest tenth. 800. Round to 800 = 28. 28427125 ≈ 28. 3

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

4 -6 Estimating Square Roots Lesson Quiz Each square root is between two integers. Name the two integers. 1. 27 5 and 6 2. – 456 – 22 and – 21 Use a calculator to find each value. Round to the nearest tenth. 3. 89 9. 4 4. 1223 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

4 -6 Estimating Square Roots 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

4 -6 Estimating Square Roots 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

4 -6 Estimating Square Roots 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. – 14 and – 15 D. – 15 and – 16