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Compare the calculations of a2 and a x 2 for various values of a.

Mathematics

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Homework (09/02/2026)
Compare these calculations:

a)

  1. Calculate 222^2.

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

    2×2=42 \times 2 = 4
  3. Compare the results.

    4=44 = 4

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

    b)

  4. Calculate 525^2.

    52=5×5=255^2 = 5 \times 5 = 25
  5. Calculate 5×25 \times 2.

    5×2=105 \times 2 = 10
  6. Compare the results.

    25>1025 > 10

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

    c)

  7. Calculate 929^2.

    92=9×9=819^2 = 9 \times 9 = 81
  8. Calculate 9×29 \times 2.

    9×2=189 \times 2 = 18
  9. Compare the results.

    81>1881 > 18

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

    Classwork (10 April 2026)
    Write the next three numbers in this cubic pattern: 1,8,271, 8, 27
    The pattern shows cubic numbers:
    1=131 = 1^3
    8=238 = 2^3
    27=3327 = 3^3
    The next three numbers will be 434^3, 535^3, and 636^3.

  10. Calculate 434^3.

    43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  11. Calculate 535^3.

    53=5×5×5=1255^3 = 5 \times 5 \times 5 = 125
  12. Calculate 636^3.

    63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216

    The next three numbers are 64,125,216\boxed{64, 125, 216}.

    Homework (10 April 2026)

    1. Calculate and fill in <,>,=:<, >, =:

    a) 23?2×32^3 \boxed{?} 2 \times 3

  13. Calculate 232^3.

    23=2×2×2=82^3 = 2 \times 2 \times 2 = 8
  14. Calculate 2×32 \times 3.

    2×3=62 \times 3 = 6
  15. Compare the results.

    8>68 > 6

    So, 23>2×32^3 \boxed{>} 2 \times 3.

    b) 13?1×1×11^3 \boxed{?} 1 \times 1 \times 1

  16. Calculate 131^3.

    13=1×1×1=11^3 = 1 \times 1 \times 1 = 1
  17. Calculate 1×1×11 \times 1 \times 1.

    1×1×1=11 \times 1 \times 1 = 1
  18. Compare the results.

    1=11 = 1

    So, 13=1×1×11^3 \boxed{=} 1 \times 1 \times 1.

    c) 125?53125 \boxed{?} 5^3

  19. Calculate 535^3.

    53=5×5×5=1255^3 = 5 \times 5 \times 5 = 125
  20. Compare the results.

    125=125125 = 125

    So, 125=53125 \boxed{=} 5^3.

    Classwork (13 April 2026)

    1. Calculate the cube roots:

    a) 273\sqrt[3]{27}

  21. Find a number that, when multiplied by itself three times, equals 27.

    3×3×3=273 \times 3 \times 3 = 27

    So, 273=3\sqrt[3]{27} = \boxed{3}.

    b) 1253\sqrt[3]{125}

  22. Find a number that, when multiplied by itself three times, equals 125.

    5×5×5=1255 \times 5 \times 5 = 125

    So, 1253=5\sqrt[3]{125} = \boxed{5}.

    Homework (13 April 2026) 2. Calculate the square roots:

    a) 4\sqrt{4}

  23. Find a number that, when multiplied by itself, equals 4.

    2×2=42 \times 2 = 4

    So, 4=2\sqrt{4} = \boxed{2}.

    b) 16\sqrt{16}

  24. Find a number that, when multiplied by itself, equals 16.

    4×4=164 \times 4 = 16

    So, 16=4\sqrt{16} = \boxed{4}.

    c) 100\sqrt{100}

  25. Find a number that, when multiplied by itself, equals 100.

    10×10=10010 \times 10 = 100

    So, 100=10\sqrt{100} = \boxed{10}.

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