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Understanding Square Roots and Perfect Squares - Math Course Lesson

This math course lesson explains how to find and evaluate square roots, as well as identify perfect squares. The lesson includes examples and practice problems. Suitable for students in Course 3.

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Understanding Square Roots and Perfect Squares - Math Course Lesson

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  1. Warm Up 1-26-09 Simplify. 1. 522. 82 64 25 225 144 3. 1224. 152 400 5. 202

  2. 4-5 Learn to find square roots. Course 3

  3. Vocabulary principal square root perfect square

  4. 62 = 36 36 = 6 Think about the relationship between the area of a square and the length of one of its sides. area = 36 square units side length = 36 = 6 units Taking the square root of a number is the inverse of squaring the number. Every positive number has two square roots, one positive and one negative. One square root of 16 is 4, since 4 • 4 = 16. The other square root of 16 is –4, since (–4) • (–4) is also 16. You can write the square roots of 16 as ±4, meaning “plus or minus” 4.

  5. + 16 = 4 – 16 = –4 Caution! –49 is not the same as – 49. A negative number has no real square root. When you press the key on a calculator, only the nonnegative square root appears. This is called the principal square root of the number. The numbers 16, 36, and 49 are examples of perfect squares. A perfect square is a number that has integers as its square roots. Other perfect squares include 1, 4, 9, 25, 64, and 81.

  6. Finding the Positive and Negative Square Roots of a Number Find the two square roots of each number.

  7. 49 = 7 225 = 15 225 = –15 49 = –7 – – 100 = 10 100 = –10 – Example 1 A. 49 7 is a square root, since 7 • 7 = 49. –7 is also a square root, since –7 • –7 = 49. B. 100 10 is a square root, since 10 • 10 = 100. –10 is also a square root, since –10 • –10 = 100. C. 225 15 is a square root, since 15 • 15 = 225. –15 is also a square root, since –15 • –15 = 225.

  8. 25 = 5 289 = 17 289 = –17 25 = –5 – – 144 = 12 144 = –12 – Example 2 A. 25 5 is a square root, since 5 • 5 = 25. –5 is also a square root, since –5 • –5 = 25. B. 144 12 is a square root, since 12 • 12 = 144. –12 is also a square root, since –12 • –12 = 144. C. 289 17 is a square root, since 17 • 17 = 289. –17 is also a square root, since –17 • –17 = 289.

  9. Perfect Square Roots:Daily GradeMemorize 1² = 12² = 43² = 94² = 165² = 256² = 367² = 498² = 649² = 8110² = 10011² = 12112² = 14413² = 16914² = 19615² = 225 16² = 25617² = 28918² = 32419² = 36120² = 40021² = 44122² = 48423² = 52924² = 57625² = 62526² = 67627² = 72928² = 78429² = 84130² = 900

  10. Evaluating Expressions Involving Square Roots Evaluate the expression.

  11. 3 36 + 7 = 3(6) + 7 3 36 + 7 Example 4 Evaluate the square root. = 18 + 7 Multiply. = 25 Add.

  12. 25 16 3 4 25 16 = 1.5625. 3 4 25 16 3 4 1.5625 + = + Example 5 + 3 4 Evaluate the square roots. = 1.25 + = 2 Add.

  13. 2 25 + 4 2 25 + 4 = 2(5) + 4 Example 6 Evaluate the square root. = 10 + 4 Multiply. = 14 Add.

  14. 18t2 1 4 18t2 18t2 1 4 = 9. + Example 7 + 1 4 9 = + 1 4 = 3 + Evaluate the square roots. 1 4 = 3 Add.

  15. Lesson Summary Find the two square roots of each number. 1. 81 2. 2500 Evaluate each expression. 3. 3 16 + 1 4. 7 9 – 2 49 ±9 ±50 13 7 5. Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft2. How much fencing does she need? 45 ft 6. Draw a Radicand 7. Draw a Radical 8. Define a Perfect Square

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