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Warm Up Simplify.

Warm Up Simplify. 1. 5 2 2. 8 2. 64. 25. 225. 144. 3. 12 2 4. 15 2. 400. 5. 20 2. 4-5. Learn to find square roots. Vocabulary. square root principal square root perfect square. 6 2 = 36 36 = 6.

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Warm Up Simplify.

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

  2. 4-5 Learn to find square roots.

  3. Vocabulary square root 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 A number that when multiplied by itself to form a product is the square rootof that product. Taking the square root of a number is the inverse of squaring the number.

  5. Caution! –49 is not the same as – 49. A negative number has no real square root. Every positive number has two square roots, one positive and one negative. The radical symbol indicates the nonnegative or principal square root. The symbol – is used to indicate the negative square root. 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. Square Roots You Should Know (Copy in Composition Notebook) √1 = 1, -1 √81 = 9, -9 √289 = 17, -17 √4 = 2, -2 √100 = 10, -10 √324 = 18, -18 √9 = 3, -3 √121 = 11 , -11 √361 = 19, -19 √16 = 4, -4 √144 = 12 , -12 √400 = 20, -20 √25 = 5, -5 √169 = 13, -13 √36 = 6, -6 √196 = 14, -14 √49 = 7, -7 √225 = 15, -15 √64 = 8, -8 √256 = 16, -16

  7. 49 = 7 49 = –7 – 100 = 10 100 = –10 – 225 = 15 225 = –15 – Additional Example: 1 Finding the Positive and Negative Square Roots of a Number Find the two square roots of each number. 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 25 = –5 – 144 = 12 144 = –12 – 289 = 17 289 = –17 – Check It Out: Example 1 Find the two square roots of each number. 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. So 169 = 13. Remember! The area of a square is s2, where s is the length of a side. Additional Example 2: Application A square window has an area of 169 square inches. How wide is the window? Write and solve an equation to find the area of the window. 132 = 169 Use the positive square root; a negative length has no meaning. The window is 13 inches wide.

  10. 16 = 4 Check It Out: Example 2 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? Write and solve an equation to find the area of the kitchen table Use the positive square root; a negative length has no meaning. So the table is 4 feet wide, which is less than 5 feet, so it will fit through the van door.

  11. 3 36 + 7 3 36 + 7 = 25 Additional Example 3A: Evaluating Expressions Involving Square Roots Simplify the expression.

  12. 25 16 3 4 25 16 3 4 + Additional Example 3B: Evaluating Expressions Involving Square Roots Simplify the expression. + = 2

  13. 2 25 + 4 2 25 + 4 = 14 Check It Out: Example 3A Simplify the expression.

  14. 18t2 1 4 18t2 1 4 + Check It Out: Example 3B Simplify the expression. + 1 4 = 3

  15. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  16. Lesson Quiz 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, -9 50, -50 7 13 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

  17. Lesson Quiz for Student Response Systems 1. Find two square roots of each number. 64 A. 4, -4 B. 8, -8 C.9, -9 D.16, -16

  18. Lesson Quiz for Student Response Systems 2. Find two square roots of each number. 6400 A. 4, -4 B. 8, -8 C.80, -80 D.800, -800

  19. Lesson Quiz for Student Response Systems 3. Evaluate the expression. A. 17 B. 17 C.19 D.72

  20. Lesson Quiz for Student Response Systems 4. Evaluate the expression. A. 4 B. 8 C.16 D.40

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