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Solve the following math problems: 1) 32 + 4 = ? 2) sqrt(16 + 9) = ? 3) 3 * sqrt(64) + 42 = ? 4) sqrt(9) + sqrt(16) = ? 5) sqrt(25) - sqrt(16) = ?

Mathematics

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Step-by-step solution

12 steps

Here are the solutions to the problems:

1)

  1. Calculate the exponent.

    32+4=9+43^2 + 4 = 9 + 4
  2. Perform the addition.

    9+4=139 + 4 = 13

    The final answer is 13\boxed{13}.

    2)

  3. Perform the addition inside the square root.

    16+9=25\sqrt{16 + 9} = \sqrt{25}
  4. Calculate the square root.

    25=5\sqrt{25} = 5

    The final answer is 5\boxed{5}.

    3)

  5. Calculate the square root.

    364+42=3×8+423\sqrt{64} + 4^2 = 3 \times 8 + 4^2
  6. Calculate the exponent.

    3×8+42=3×8+163 \times 8 + 4^2 = 3 \times 8 + 16
  7. Perform the multiplication.

    3×8+16=24+163 \times 8 + 16 = 24 + 16
  8. Perform the addition.

    24+16=4024 + 16 = 40

    The final answer is 40\boxed{40}.

    4)

  9. Calculate each square root separately.

    9+16=3+4\sqrt{9} + \sqrt{16} = 3 + 4
  10. Perform the addition.

    3+4=73 + 4 = 7

    The final answer is 7\boxed{7}.

    5)

  11. Calculate each square root separately.

    25−16=5−4\sqrt{25} - \sqrt{16} = 5 - 4
  12. Perform the subtraction.

    5−4=15 - 4 = 1

    The final answer is 1\boxed{1}.

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