Slide1 : Finding Square Roots
Slide2 : 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. Objective:
Learn to estimate square roots to a given number of decimal places and solve problems using square roots. Square Root
Slide3 : Additional Example 1A: Estimating Square Roots of Numbers Each square root is between two integers. Name the integers. 55 Think: What are perfect squares close to 55? 72 = 49 49 < 55 82 = 64 64 > 55 A.
Slide4 : 90 – Additional Example 1B: Estimating Square Roots of Numbers Continued Think: What are perfect squares close to 90? –92 = 81 81 < 90 –102 = 100 100 > 90 Each square root is between two integers. Name the integers. B.
Slide5 : Try This: Example 1A Each square root is between two integers. Name the integers. 80 Think: What are perfect squares close to 80? 82 = 64 64 < 80 92 = 81 81 > 80 A.
Slide6 : 45 – Each square root is between two integers. Name the integers. Think: What are perfect squares close to 45? –62 = 36 36 < 45 –72 = 49 49 > 45 B. Try This: Example 1B
Slide7 : 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.
Slide8 : Additional Example 2 Continued
Slide9 : Because 500 is between 222 and 232, the square root of 500 is between 22 and 23. The square root is between 22.3 and 22.4. Additional Example 2 Continued
Slide10 : Consider 22.35. 22.352 = 499.5225 Too low The square root must be greater than 22.35, so round up. 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
Slide11 : 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
Slide12 : 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. Additional Example 2 Continued
Slide13 : 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 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.
Slide14 : Try This: Example 2 Continued
Slide15 : Because 250 is between 152 and 162, the square root of 250 is between 15 and 16. 1 2 3 4 The square root is between 15.8 and 15.9. Try This: Example 2 Continued
Slide16 : Consider 15.85. 15.852 = 251.2225 The square root is lower than 15.85, so round down. The length of each side of the garden is about 15.8 ft. To round to the nearest tenth, look at the next decimal place. Try This: Example 2 Continued
Slide17 : 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. Solve 4 • 15.8 = 63.2 Perimeter 4 • side You will need about 63.2 feet of fence. Try This: Example 2 Continued
Slide18 : 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. Try This: Example 2 Continued
Slide19 : Additional Examples 3: Using a Calculator to Estimate the Value of a Square Root Using a calculator, 500 ≈ 22.36067977…. Rounded, 500 is 22.4. Use a calculator to find 500. Round to the nearest tenth.
Slide20 : Try This: Example 3 Rounded, 200 is 14.1. Use a calculator to find 200. Round to the nearest tenth.
Slide21 : 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 9.4 35.0 179 ft