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Identify the pattern. The given numbers are 1²=1, 2²=4, 3²=9.

Mathematics

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Here are the solutions to the problems:

4. Find the next six square numbers in this pattern: 1; 4; 9.

  1. Identify the pattern.

    The given numbers are 12=11^2=1, 22=42^2=4, 32=93^2=9.

  2. Calculate the next six square numbers.

    42=164^2 = 16
    52=255^2 = 25
    62=366^2 = 36
    72=497^2 = 49
    82=648^2 = 64
    92=819^2 = 81
    The next six square numbers are 16,25,36,49,64,81\boxed{16, 25, 36, 49, 64, 81}.

    5. Calculate:

    a)

  3. Calculate the square.

    52=5×5=255^2 = 5 \times 5 = \boxed{25}

    b)

  4. Calculate the square.

    82=8×8=648^2 = 8 \times 8 = \boxed{64}

    d)

  5. Calculate the square.

    102=10×10=10010^2 = 10 \times 10 = \boxed{100}

    e)

  6. Calculate the square.

    112=11×11=12111^2 = 11 \times 11 = \boxed{121}

    6. Compare these calculations. Fill in >>; <<; ==.

    a)

  7. Calculate both sides.

    22=2×2=42^2 = 2 \times 2 = 4
    2×2=42 \times 2 = 4

  8. Compare the results.

    4=44 = 4
    So, 22=2×22^2 \boxed{=} 2 \times 2.

    b)

  9. Calculate both sides.

    52=5×5=255^2 = 5 \times 5 = 25
    5×2=105 \times 2 = 10

  10. Compare the results.

    25>1025 > 10
    So, 52>5×25^2 \boxed{>} 5 \times 2.

    d)

  11. Calculate both sides.

    92=9×9=819^2 = 9 \times 9 = 81
    9×2=189 \times 2 = 18

  12. Compare the results.

    81>1881 > 18
    So, 92>9×29^2 \boxed{>} 9 \times 2.

    e)

  13. Calculate both sides.

    11×11=12111 \times 11 = 121
    112=11×11=12111^2 = 11 \times 11 = 121

  14. Compare the results.

    121=121121 = 121
    So, 11×11=11211 \times 11 \boxed{=} 11^2.

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