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Pre-Algebra 3-9 Finding Square Roots Student Learning Goal Chart Lesson Reflections 3-9

Pre-Algebra Learning Goal Students will understand rational and real numbers.

Students will understand rational and real numbers by being able to do the following: Learn to write rational numbers in equivalent forms (3.1) Learn to add and subtract decimals and rational numbers with like denominators (3.2) Learn to add and subtract fractions with unlike denominators (3.5) Learn to multiply fractions, decimals, and mixed numbers (3.3) Learn to divide fractions and decimals (3.4) Learn to solve equations with rational numbers (3.6) Learn to solve inequalities with rational numbers (3-7) Learn to find square roots (3-8) Learn to estimate square roots to a given number of decimal places and solve problems using square roots (3-9)

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

Pre-Algebra 3-9 Finding Square Roots Pre-Algebra HW Page 152 #19-38 all

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

Pre-Algebra 3-9 Finding Square Roots Warm Up Find the two square roots of each number. Evaluate each expression. Pre-Algebra 3-9 Finding Square Roots 12

Pre-Algebra 3-9 Finding 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

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

Pre-Algebra 3-9 Finding Square Roots 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.

Pre-Algebra 3-9 Finding Square Roots 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? 7 2 = < = > 55 7 < 55 < 8 55 is between 7 and 8. A.

Pre-Algebra 3-9 Finding Square Roots 90 – Additional Example 1B: Estimating Square Roots of Numbers Continued Think: What are perfect squares close to 90? –9 2 = < 90 –10 2 = > 90 –9 < – 90 < –10 Each square root is between two integers. Name the integers. 90 – is between –9 and –10. B.

Pre-Algebra 3-9 Finding Square Roots Try This: Example 1A Each square root is between two integers. Name the integers. 80 Think: What are perfect squares close to 80? 8 2 = < = > 80 8 < 80 < 9 is between 8 and A.

Pre-Algebra 3-9 Finding Square Roots 45 – Each square root is between two integers. Name the integers. Think: What are perfect squares close to 45? –6 2 = < 45 –7 2 = > 45 –6 < – 45 < –7 45 – is between –6 and –7. B. Try This: Example 1B

Pre-Algebra 3-9 Finding 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

Pre-Algebra 3-9 Finding 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.

Pre-Algebra 3-9 Finding 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 = Guess Square root is between 22.2 and 22.5 Too low = Guess Square root is between 22.2 and 22.4 Too high = Guess Square root is between 22.3 and 22.4 Too low = Guess The square root is between 22.3 and Additional Example 2 Continued

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

Pre-Algebra 3-9 Finding 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 = 89.6 Perimeter 4 side You will need about 89.6 inches of fringe. Additional Example 2 Continued

Pre-Algebra 3-9 Finding Square Roots The length 90 inches divided by 4 is 22.5 inches. A 22.5-inch square has an area of square inches, which is close to 500, so the answers are reasonable. Look Back Additional Example 2 Continued

Pre-Algebra 3-9 Finding 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 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. Understand the Problem

Pre-Algebra 3-9 Finding Square Roots 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 Try This: Example 2 Continued

Pre-Algebra 3-9 Finding Square Roots Because 250 is between 15 2 and 16 2, the square root of 250 is between 15 and 16. Solve The square root is between 15.8 and Guess = Too Low Square root is between 15.5 and 16 Guess = Too high Square root is between 15.5 and 15.9 Guess = Too Low Square root is between 15.7 and 15.9 Guess = Too Low Square root is between 15.8 and 15.9 Try This: Example 2 Continued

Pre-Algebra 3-9 Finding Square Roots Consider = The square root is lower than 15.85, so round down. To the nearest tenth, 250 is about Solve 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

Pre-Algebra 3-9 Finding Square Roots 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 = 63.2 Perimeter 4 side You will need about 63.2 feet of fence. Try This: Example 2 Continued

Pre-Algebra 3-9 Finding Square Roots The length 63.2 feet divided by 4 is 15.8 feet. A 15.8 foot square has an area of square feet, which is close to 250, so the answers are reasonable. Look Back Try This: Example 2 Continued

Pre-Algebra 3-9 Finding Square Roots Additional Examples 3: Using a Calculator to Estimate the Value of a Square Root Using a calculator, 500 ≈ …. Rounded, 500 is Use a calculator to find 500. Round to the nearest tenth.

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

Pre-Algebra 3-9 Finding Square Roots Lesson Quiz Each square root is between two integers. Name the two integers – 456 Use a calculator to find each value. Round to the nearest tenth 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 – ft