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Calculate the following expressions, rounding to four decimal places: (d) (1.789)3 * (13.79)2 / 318.2 (e) sqrt(151.8) + cbrt(73.85) / 2.3762 (f) (9.683)3 + sqrt(89.74) / cbrt(198.5 - 0.94372)

Mathematics

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Answers

3 parts
d

3.4211\text{3.4211}

e

2.9256\text{2.9256}

f

157.3200\text{157.3200}

Step-by-step solution

13 steps

here are the solutions to the problems.

Part d· 4 steps

  1. Evaluate (1.789)3(1.789)^3.

    (1.789)3=1.789×1.789×1.789≈5.723959609(1.789)^3 = 1.789 \times 1.789 \times 1.789 \approx 5.723959609

  2. Evaluate (13.79)2(13.79)^2.

    (13.79)2=13.79×13.79=190.1641(13.79)^2 = 13.79 \times 13.79 = 190.1641

  3. Multiply the terms in the numerator.

    5.723959609×190.1641≈1088.583065.723959609 \times 190.1641 \approx 1088.58306

  4. Divide the numerator by the denominator.

    1088.58306318.2≈3.4210655\frac{1088.58306}{318.2} \approx 3.4210655

    Rounding to four decimal places:

    3.4211\boxed{\text{3.4211}}

Part e

2.9256\text{2.9256}

  1. Evaluate the square root and cube root in the numerator.

    151.8≈12.3190016\sqrt{151.8} \approx 12.3190016 73.853≈4.1969630\sqrt[3]{73.85} \approx 4.1969630

  2. Add the terms in the numerator.

    12.3190016+4.1969630=16.515964612.3190016 + 4.1969630 = 16.5159646

  3. Evaluate the term in the denominator.

    2.3762=5.6453762.376^2 = 5.645376

  4. Divide the numerator by the denominator.

    16.51596465.645376≈2.925600\frac{16.5159646}{5.645376} \approx 2.925600

    Rounding to four decimal places:

    2.9256\boxed{\text{2.9256}}

Part f

157.3200\text{157.3200}

  1. Evaluate the terms in the numerator.

    (9.683)3≈906.908000(9.683)^3 \approx 906.908000 89.74≈9.4731200\sqrt{89.74} \approx 9.4731200

  2. Add the terms in the numerator.

    906.908000+9.4731200=916.381120906.908000 + 9.4731200 = 916.381120

  3. Evaluate the term inside the cube root in the denominator.

    (0.9437)2=0.89057969(0.9437)^2 = 0.89057969 198.5−0.89057969=197.60942031198.5 - 0.89057969 = 197.60942031

  4. Evaluate the cube root in the denominator.

    197.609420313≈5.8248090\sqrt[3]{197.60942031} \approx 5.8248090

  5. Divide the numerator by the denominator.

    916.3811205.8248090≈157.32000\frac{916.381120}{5.8248090} \approx 157.32000

    Rounding to four decimal places:

    157.3200\boxed{\text{157.3200}}
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