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1, 4, 9 and 16 are perfect squares.

1, 4, 9 and 16 are perfect squares. . Can you find more?. In this lesson, you will learn how to generate perfect squares by exploring a visual and learning a definition. S ● S = A. S . S 2 = A. S . Integers: Include whole numbers and their opposites.

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1, 4, 9 and 16 are perfect squares.

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  1. 1, 4, 9 and 16 are perfect squares. Can you find more?

  2. In this lesson, you will learn how to generate perfect squaresby exploring a visual and learning a definition.

  3. S ● S = A S S2 = A S

  4. Integers: Include whole numbers and their opposites Examples: -3, -2, -1, 0, 1, 2, 3

  5. Perfect Square: Area of a square with an integer side length 2 4 3 2 1 1 Irrational number side lengths 2 1

  6. Perfect Square: Area of a square with an integer side length Perfect Square Integer P.S. = Int. ● Int. P.S. = (Integer)2 Integer

  7. Perfect Square: The result of squaring an integer 12 = 1 62 = 36 112 = 121 162 = 256 22 = 4 72 = 49 122 = 144 172 = 289 32 = 9 82 = 64 132 = 169 182 = 324 42 = 16 92 = 81 142 = 196 192 = 361 52 = 25 102 = 100 152 = 225 202 = 400

  8. Negative Perfect Squares? Perfect Square: Area of a square with an integer side length Perfect Square: The result of squaring an integer (-2)2 = (-2)(-2) = 4 There are no negative perfect squares.

  9. Is zero a perfect square? Perfect Square: Area of a square with an integer side length Perfect Square: The result of squaring an integer (0)2 = (0)(0) = 0 Zero is a perfect square.

  10. Are all even numbers perfect squares? 42 = 8 42 = 4 ● 2 = 8 42 = 16 42 = 4 ● 4 Not all even numbers are perfect squares.

  11. Perfect Square: The result of squaring an integer 12 = 1 62 = 36 112 = 121 162 = 256 22 = 4 72 = 49 122 = 144 172 = 289 32 = 9 82 = 64 132 = 169 182 = 324 42 = 16 92 = 81 142 = 196 192 = 361 52 = 25 102 = 100 152 = 225 202 = 400

  12. In this lesson, you have learned how to generate perfect squaresby exploring a visual and learning a definition.

  13. Is 40 a perfect square?

  14. How many perfect squares are there between 200 and 300?

  15. While squaring a number means to multiply a number by itself, cubing a number means to multiply a number by itself three times. So a perfect cube is the result of cubing an integer. This means 8 is a perfect cube because 2 x 2 x 2 = 8. How many perfect cubes are there between 0 and 1000?

  16. Find as many sets of three perfect squares where the largest of the three perfect squares is the sum of the two smaller perfect squares. For example, one set is 9, 16, 25 because 9 + 16 = 25.

  17. Which of the following is a perfect square? (a) 600 (b) 700 (c) 800 (d) 900 How many perfect squares are there between 300 and 500?

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