Square and square roots

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Square and square roots

  1. 1. a qu S s re and Sq uar Roo e ts
  2. 2. We will: • Understand the meaning of squaring a number and finding the square root of a number • Find squares of numbers • Raise a whole number to a whole number power • Find square roots of perfect squares • Find approximate square roots of nonperfect squares
  3. 3. 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.
  4. 4. 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 = ____
  5. 5. Talk to the person next to you 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?
  6. 6. If a square measures 4 inches on each side, how would you find its area? 4 inches 4 inches 4 inches 4 inches
  7. 7. Remember how to calculate the area? 4 inches 4 inches A=l•w A = 4 in. • 4 in. A = 16 in. 2
  8. 8. A square must have the same length and width. 4 inches 4 inches A=l•w A = 4 in. • 4 in.
  9. 9. Square Number • Also called a “perfect square” • A number that is the square of a whole number • Can be represented by arranging objects in a square.
  10. 10. Square Numbers
  11. 11. To square a number means to multiply it by itself. 5 squared means 5 x 5 Take the number 5 And square it!
  12. 12. There is a shorter way to write 5 x 5. Say: “5 squared” or “5 to the 2nd power”.
  13. 13. These are the parts. This is the base This is the exponent
  14. 14. This is another formula for finding the area of a square. s A=s 2 s is the side length
  15. 15. Evaluate it! A. 14 B. 49
  16. 16. Try these: Number Squared 2 9 11 2 3 2 10 2 Factors Standard Form 9 • 9 11• 11 3 • 3 10 • 10 81 121 9 100
  17. 17. These numbers are called perfect squares
  18. 18. If a number is a perfect square, then you can find its exact square root. A perfect square is simply a number that can be written as the square of another number.
  19. 19. What are the first 10 whole numbers that are perfect squares? 2 2 2 2 2 2 2 2 2 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 2
  20. 20. -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. 62 = 36 36 = 6
  21. 21. The symbol used to indicate a root is the radical symbol -
  22. 22. Every radical expression has three parts… • Radical symbol • Index • Radicand
  23. 23. Every radical expression has Radical three parts… Index 2 49 Radicand
  24. 24. The index of a radical is a whole number greater than or equal to 2.
  25. 25. The index of a square root is always 2.
  26. 26. The square root of 49 could 2 be written as 49 … but is normally written as 49 .
  27. 27. What does square root mean?
  28. 28. The square root of a number is another number which when multiplied by itself gives back the original number.
  29. 29. What is a square root? ? the measure of the side of the square 16 = 4
  30. 30. What is the square root of 36? 36 = 6
  31. 31. Example: 49 = 7 because 7 ⋅ 7 = 7 = 49 2 Also 49 = − 7 because ( − 7 )( − 7 ) = ( − 7 ) = 49 2
  32. 32. Find the two square roots of each number. A. 49 – 49 = 7 49 = –7 B. 100 100 = 10 – 100 = –10 7 is a square root, since 7 • 7 = 49. –7 is also a square root, since –7 • –7 = 49. 10 is a square root, since 10 • 10 = 100. –10 is also a square root, since –10 • –10 = 100.
  33. 33. Find the two square roots of each number. A. 25 – 25 = 5 25 = –5 B. 144 144 = 12 5 is a square root, since 5 • 5 = 25. –5 is also a square root, since –5 • –5 = 25. 12 is a square root, since 12 • 12 = 144. – 144 = –12 –12 is also a square root, since –12 • –12 = 144.
  34. 34. Open your books to page 72 so we can try some problems together

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