1. Course 3 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

2. Course 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

3. Course 3 4-6 Estimating Square Roots Learn to estimate square roots to a given number of decimal places and solve problems using square roots. Course 3 4-6 TB P. 186-189

4. Course 3 4-6 Estimating Square Roots Additional Example 1A: Estimating Square Roots of Numbers Each 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.

5. Course 3 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 Each 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 –

6. Course 3 4-6 Estimating Square Roots First find the length of a side. Then you can use the length of a side to find the perimeter, the length of fringe around the tablecloth. Additional Example 2: Problem Solving 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 tenth of an inch. Understand the Problem

7. Course 3 4-6 Estimating Square Roots Additional Example 2 Continued Make a Plan The length of a side, in feet, is the number that you multiply by itself to get 500. To be accurate, find this number to the nearest tenth. If you do not know a step-by-step method for finding 500, use guess and check.

8. Course 3 4-6 Estimating Square Roots Because 500 is between 22 2 and 23 2, the square root of 500 is between 22 and 23. Solve Square root is between 22 and 22.5 Too high 22.5 2 = 506.25 Guess 22.5 1 Square root is between 22.2 and 22.5 Too low 22.2 2 = 492.84 Guess 22.2 2 Square root is between 22.2 and 22.4 Too high 22.4 2 = 501.76 Guess 22.4 3 Square root is between 22.3 and 22.4 Too low 22.3 2 = 497.29 Guess 22.3 4 22.022.222.422.6 The square root is between 22.3 and 22.4. Additional Example 2 Continued

9. Course 3 4-6 Estimating Square Roots Consider 22.35. 22.35 2 = 499.5225 Too low The square root must be greater than 22.35, so round up. To the nearest tenth, 500 is about 22.4. Solve The length of each side of the table is about 22.4 in. The square root is between 22.3 and 22.4. To round to the nearest tenth, look at the next decimal place. Additional Example 2 Continued

10. Course 3 4-6 Estimating Square Roots The length of a side of the tablecloth is 22.4 inches, to the nearest tenth of an inch. Now estimate the length around the tablecloth. Solve 4 22.4 = 89.6 Perimeter = 4 side You will need about 89.6 inches of fringe. Additional Example 2 Continued

11. Course 3 4-6 Estimating Square Roots The length 90 inches divided by 4 is 22.5 inches. A 22.5-inch square has an area of 506.25 square inches, which is close to 500, so the answers are reasonable. Look Back Additional Example 2 Continued

12. Course 3 4-6 Estimating Square Roots Additional Example 3: 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.

13. Course 3 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