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## Warm Up 1-26-09 Simplify.

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**Warm Up 1-26-09**Simplify. 1. 522. 82 64 25 225 144 3. 1224. 152 400 5. 202**4-5**Learn to find square roots. Course 3**Vocabulary**principal square root perfect square**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.**+ 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.**Finding the Positive and Negative Square Roots of a Number**Find the two square roots of each number.**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.**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.**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**Evaluating Expressions Involving Square Roots**Evaluate the expression.**3 36 + 7 = 3(6) + 7**3 36 + 7 Example 4 Evaluate the square root. = 18 + 7 Multiply. = 25 Add.**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.**2 25 + 4**2 25 + 4 = 2(5) + 4 Example 6 Evaluate the square root. = 10 + 4 Multiply. = 14 Add.**18t2**1 4 18t2 18t2 1 4 = 9. + Example 7 + 1 4 9 = + 1 4 = 3 + Evaluate the square roots. 1 4 = 3 Add.**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