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Pre-Algebra

Learn to estimate square roots to a given number of decimal places and solve problems using square roots. 3-9. Finding Square Roots. Pre-Algebra. Finding Square Roots. 3-9. Finding Square Roots. Pre-Algebra.

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Pre-Algebra

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  1. Learn to estimate square roots to a given number of decimal places and solve problems using square roots. 3-9 Finding Square Roots Pre-Algebra Finding Square Roots

  2. 3-9 Finding Square Roots Pre-Algebra A museum director wants to install a skylight to illuminate an unusual piece of art. It must be square and have an area of 300 square inches, with wood trim around it. Can you calculate the trim that you need? You can do this by using your knowledge of squares and square roots.

  3. 7 < 55 < 8 55 is between 7 and 8. 3-9 Finding Square Roots Pre-Algebra 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? 55 A. 49 < 55 72 = 49 64 > 55 82 = 64

  4. – –9 < – 90 < –10 90 3-9 is between –9 and –10. Finding Square Roots Pre-Algebra 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 81 < 90 –92 = 81 100 > 90 –102 = 100

  5. 3-9 Finding Square Roots Pre-Algebra 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.

  6. Understand the Problem 3-9 Finding Square Roots Pre-Algebra 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. 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.

  7. 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. Make a Plan 3-9 Finding Square Roots Pre-Algebra Example 2 Continued

  8. 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 findl = 500 Make a Plan 3-9 Finding Square Roots Pre-Algebra Example 2 Continued

  9. To the nearest tenth, 500 is about 22.4. Solve 3-9 Finding Square Roots Pre-Algebra Additional Example 2 Continued The length of each side of the table is about 22.4 in.

  10. 3-9 Finding Square Roots Pre-Algebra 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.

  11. 3-9 Finding Square Roots Look Back Pre-Algebra Example 2 Continued 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.

  12. 8 < 80 < 9 is between 8 and 9. 80 3-9 Finding Square Roots Pre-Algebra Try This: Example 1A Each square root is between two integers. Name the integers. Think: What are perfect squares close to 80? A. 80 64 < 80 82 = 64 81 > 80 92 = 81

  13. Using a calculator, 200 ≈ 14.14213562…. 3-9 Finding Square Roots Pre-Algebra Try This: Example 3 Use a calculator to find 200. Round to the nearest tenth. Rounded, 200 is 14.1.

  14. Understand the Problem 3-9 Finding Square Roots Pre-Algebra 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. 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.

  15. The length of a side, in feet, is the number that you multiply by itself to get 250. To be accurate, find this number to the nearest tenth. If you do not know a step-by-step method for finding 250, use guess and check. Make a Plan 3-9 Finding Square Roots Pre-Algebra Try This: Example 2 Continued

  16. 3-9 Finding Square Roots Pre-Algebra Try This: Example 2 Continued Solve The length of a side of the garden is 15.8 feet, to the nearest tenth of a foot. Now estimate the length around the garden. 4 • 15.8 = 63.2 Perimeter = 4 • side You will need about 63.2 feet of fence.

  17. 3-9 Finding Square Roots Look Back Pre-Algebra Try This: Example 2 Continued 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.

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