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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up Simplify. 8. Write the rule in words and as an equation. 64. 1. 5 2 2. 8 2. 25. 3. 12 2 4. 15 2. 144. 225. 5. 20 2. 400. 6. Evaluate (–3) 4. 81.

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up Simplify. 8. Write the rule in words and as an equation. 64 1. 522. 82 25 3. 1224. 152 144 225 5. 202. 400 6. Evaluate (–3)4 81 7.Evaluate gh + 3k – gkfor g = 2, h = 4, and k = 3. 7

  3. CMT Question of the day! And Check Homework…

  4. 5.3  10–3 5.7  107 4-4 Lesson Quiz Write each number in standard notation. 1. 1.72  104 17,200 2. 6.9  10–3 0.0069 Write each number in scientific notation. 3. 0.0053 4. 57,000,000 5. Write the rule in words and as an equation. T Divide by 2, Y = x/2

  5. 4-5 Learn to find square roots.

  6. Shade in graph paper to make each of the shapes below. Each shape is a square. Count and write the number of square tiles in each of the larger squares below. 1. 2. 3.

  7. Count and write the number of square tiles in each of the larger squares below. 1. 2. 3. Continue to draw larger squares. Make one that is 7 tiles wide and 7 tiles high; then make one that is 8 wide and 8 high. Count the number of squares in each shape. 4. 7 by 7 = ___________ 5. 8 by 8 = ______________

  8. Continue to draw larger squares. Make one that is 7 tiles wide and 7 tiles high; then make one that is 8 wide and 8 high. Count the number of squares in each shape. 4. 7 by 7 = ____ 5. 8 by 8 = _______ Talk in your groups about the following questions. Be prepared to discuss them if I call on you. The numbers 1, 4, 9, 16, 25, etc. are known as perfect squares. Why do you think they are called perfect squares?How are the width and the height of the squares related? How are they related to the total number of tiles?How could you find the next numbers that are perfect squares without tiles?

  9. Try This Write down the first 10 perfect squares, starting with 0. 0, 1, 4, 9, ___, ___, ___, ___, ___, ___Now subtract each number from the one after it. 1 , 3 , 5 , ___, ___, ___, ___, ___What pattern do you see in the difference between two perfect squares? Use your answer from Exercise 3 above to find all perfect squares less than 200.

  10. 62 = 36 36 = 6 -What’s the opposite operation to addition? -What’s the opposite operation to multiplication? -The opposite operation to squaring a number is taking the square root.

  11. 49 = 7 49 = –7 – 100 = 10 100 = –10 – 225 = 15 225 = –15 – 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.

  12. 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.

  13. 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.

  14. 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.

  15. 3 36 + 7 3 36 + 7 = 3(6) + 7 Additional Example 3A: Evaluating Expressions Involving Square Roots Simplify the expression. Evaluate the square root. = 18 + 7 Multiply. = 25 Add.

  16. 25 16 3 4 3 4 25 16 25 16 3 4 = 1.5625. 1.5625 + = + Additional Example 3B: Evaluating Expressions Involving Square Roots Simplify the expression. + 3 4 Evaluate the square roots. = 1.25 + = 2 Add.

  17. 2 25 + 4 2 25 + 4 = 2(5) + 4 Check It Out: Example 3A Simplify the expression. Evaluate the square root. = 10 + 4 Multiply. = 14 Add.

  18. 18t2 1 4 18t2 18t2 1 4 = 9. + Check It Out: Example 3B Simplify the expression. + 1 4 9 = + 1 4 = 3 + Evaluate the square roots. 1 4 = 3 Add.

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

  20. 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 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

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

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

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

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

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