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Square Roots Estimation Course: Understanding Squares & Expressions

Learn to estimate square roots of numbers to solve problems. Understand perfect squares, estimate using calculators, and apply the knowledge. Practice estimating large square roots in various scenarios. Gain confidence in evaluating expressions involving square roots efficiently.

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Square Roots Estimation Course: Understanding Squares & Expressions

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  1. 3. 8+ 144 4. 7 289 Warm Up Find the two square roots of each number. Evaluate each expression. 1. 144 2. 256 ±12 ±16 20 119 5. A square window has an area of 169 square inches, how wide is the window? 6. A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?

  2. 4-6 Learn to estimate square roots to a given number of decimal places and solve problems using square roots. Course 3

  3. Estimating Square Roots of Numbers Each square root is between two integers. Name the integers. Explain your answer.

  4. 55 is between 7 and 8 because 55 is between 49 and 64. Example 1 Think: What are perfect squares close to 55? 55 49 < 55 72 = 49 64 > 55 82 = 64

  5. – is between –9 and –10 because 90 is between 81 and 100. 90 Example 2 Think: What are perfect squares close to 90? – 90 81 < 90 –92 = 81 100 > 90 –102 = 100

  6. 80 is between 8 and 9 because 80 is between 64 and 81. Example 3 Think: What are perfect squares close to 80? 80 64 < 80 82 = 64 81 > 80 92 = 81

  7. – is between –6 and –7 because 45 is between 36 and 49. 45 Example 4 Think: What are perfect squares close to 45? – 45 36 < 45 –62 = 36 49 > 45 –72 = 49

  8. Estimating Large Square Roots Use a calculator to find answer, round to the nearest tenth.

  9. Example 5 Use a calculator to find 600. Round to the nearest tenth. Using a calculator, 600 ≈ 24.49489742…. Rounded, 600 is 24.5.

  10. Using a calculator, 800 ≈ 28.2842712…. Example 6 Use a calculator to find 800. Round to the nearest tenth. Rounded, 800 is 28.3.

  11. Lesson Summary 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. 9.4 35.0 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? 179 ft

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