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Calculate the following expressions involving square roots, parentheses, and basic arithmetic operations.

Mathematics

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21 steps

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Calculate.

a) 4+(5−6)\sqrt{4} + (5-6)

  1. Calculate the square root and the expression inside the parentheses.

    2+(−1)2 + (-1)
  2. Perform the addition.

    11

    The result is 1\boxed{1}.

    b) 64−(5−6)\sqrt{64} - (5-6)

  3. Calculate the square root and the expression inside the parentheses.

    8−(−1)8 - (-1)
  4. Perform the subtraction.

    8+18 + 1 99

    The result is 9\boxed{9}.

    c) (8−10)+36(8-10) + \sqrt{36}

  5. Calculate the expression inside the parentheses and the square root.

    (−2)+6(-2) + 6
  6. Perform the addition.

    44

    The result is 4\boxed{4}.

    d) (8−12)+8(8-12) + \sqrt{8}

  7. Calculate the expression inside the parentheses and simplify the square root.

    (−4)+4×2(-4) + \sqrt{4 \times 2} −4+22-4 + 2\sqrt{2}

    The result is −4+22\boxed{-4 + 2\sqrt{2}}.

    e) 1253−(6−9)\sqrt[3]{125} - (6-9)

  8. Calculate the cube root and the expression inside the parentheses.

    5−(−3)5 - (-3)
  9. Perform the subtraction.

    5+35 + 3 88

    The result is 8\boxed{8}.

    f) (−4−7)+9(-4-7) + \sqrt{9}

  10. Calculate the expression inside the parentheses and the square root.

    (−11)+3(-11) + 3
  11. Perform the addition.

    −8-8

    The result is −8\boxed{-8}.

    3. Calculate.

    a) 25+(5+4)+(62)\sqrt{25} + (5+4) + (6^2)

  12. Calculate the square root, expression in parentheses, and exponent.

    5+9+365 + 9 + 36
  13. Perform the additions from left to right.

    14+3614 + 36 5050

    The result is 50\boxed{50}.

    b) (9)+36−(6+2)(\sqrt{9}) + \sqrt{36} - (6+2)

  14. Calculate the square roots and expression in parentheses.

    3+6−83 + 6 - 8
  15. Perform the operations from left to right.

    9−89 - 8 11

    The result is 1\boxed{1}.

    c) 125+(3)+(5−6)\sqrt{125} + (3) + (5-6)

  16. Simplify the square root and calculate the expression in parentheses.

    25×5+3+(−1)\sqrt{25 \times 5} + 3 + (-1) 55+3−15\sqrt{5} + 3 - 1
  17. Perform the addition and subtraction.

    55+25\sqrt{5} + 2

    The result is 55+2\boxed{5\sqrt{5} + 2}.

    d) (5+4)−(53)−(83)(5+4) - (5^3) - (\sqrt[3]{8})

  18. Calculate the expression in parentheses, exponent, and cube root.

    9−125−29 - 125 - 2
  19. Perform the subtractions from left to right.

    −116−2-116 - 2 −118-118

    The result is −118\boxed{-118}.

    e) (10−5)+(81)−(62)(10-5) + (\sqrt{81}) - (6^2)

  20. Calculate the expression in parentheses, square root, and exponent.

    5+9−365 + 9 - 36
  21. Step 21

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