3-9 Finding Square Roots Warm Up Problem of the Day Lesson Presentation Pre-Algebra

Finding Square Roots Learn to estimate square roots to a given number of decimal places and solve problems using square roots.

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

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

Try This: Example 1A Each square root is between two integers. Name the integers. Think: What are perfect squares close to 80? A. 80 82 = 64 64 < 80 92 = 81 81 > 80 is between 8 and 9. 80 8 < 80 < 9

Try This: Example 1B Each square root is between two integers. Name the integers. Think: What are perfect squares close to 45? B. – 45 –62 = 36 36 < 45 –72 = 49 49 > 45 45 – is between –6 and –7. –6 < – 45 < –7

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 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 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.

Additional Example 2 Continued Solve Because 500 is between 222 and 232, the square root of 500 is between 22 and 23. Square root is between 22 and 22.5 Too high 22.52 = 506.25 Guess 22.5 1 Square root is between 22.2 and 22.5 Too low 22.22 = 492.84 Guess 22.2 2 Square root is between 22.3 and 22.4 Too low 22.32 = 497.29 Guess 22.3 4 Square root is between 22.2 and 22.4 Too high 22.42 = 501.76 Guess 22.4 3 22.0 22.2 22.4 22.6 The square root is between 22.3 and 22.4.

Additional Example 2 Continued Solve The square root is between 22.3 and 22.4. To round to the nearest tenth, look at the next decimal place. Consider 22.35. 22.352 = 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. The length of each side of the table is about 22.4 in.

Additional Example 2 Continued Solve 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. 4 • 22.4 = 89.6 Perimeter 4 • side You will need about 89.6 inches of fringe.

Additional Example 2 Continued Look Back 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.

Use a calculator to find 500. Round to the nearest tenth. Additional Examples 3: Using a Calculator to Estimate the Value of a Square Root Use a calculator to find 500. Round to the nearest tenth. Using a calculator, 500 ≈ 22.36067977…. Rounded, 500 is 22.4.

Use a calculator to find 200. Round to the nearest tenth. Try This: Example 3 Use a calculator to find 200. Round to the nearest tenth. Using a calculator, 200 ≈ 14.14213562…. Rounded, 200 is 14.1.

Try This: 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. Understand the Problem First find the length of a side. Then you can use the length of a side to find the perimeter, the length of the fence.

Try This: Example 2 Continued Look Back The length 63.2 feet divided by 4 is 15.8 feet. A 15.8 foot square has an area of 249.64 square feet, which is close to 250, so the answers are reasonable.

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