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What is the difference between the square root of 4 1/4 and the square root of 9/16? Evaluate sqrt(0.000441). Work out the square root of 0.2809. Evaluate 216 / 6/13. Work out 13/28 / 4 4/13. Find the value of 4 1/3 x 9/26 x 8/27

Mathematics

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10) What is the difference between the square of 4144 \frac{1}{4} and the square root of 79167 \frac{9}{16}?

  1. Convert mixed numbers to improper fractions.

    414=4×4+14=1744 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4} 7916=7×16+916=112+916=121167 \frac{9}{16} = \frac{7 \times 16 + 9}{16} = \frac{112 + 9}{16} = \frac{121}{16}

  2. Calculate the square of 4144 \frac{1}{4}.

    (174)2=17242=28916\left(\frac{17}{4}\right)^2 = \frac{17^2}{4^2} = \frac{289}{16}

  3. Calculate the square root of 79167 \frac{9}{16}.

    12116=12116=114\sqrt{\frac{121}{16}} = \frac{\sqrt{121}}{\sqrt{16}} = \frac{11}{4}

  4. Find the difference between the two values.

    28916−114\frac{289}{16} - \frac{11}{4}

    To subtract, find a common denominator, which is 16.

    114=11×44×4=4416\frac{11}{4} = \frac{11 \times 4}{4 \times 4} = \frac{44}{16} 28916−4416=289−4416=24516\frac{289}{16} - \frac{44}{16} = \frac{289 - 44}{16} = \frac{245}{16}

  5. Convert the improper fraction to a mixed number.

    24516=15516\frac{245}{16} = 15 \frac{5}{16}

    The difference is 15516\boxed{\mathbf{15 \frac{5}{16}}}.

    11) Evaluate 0.000441\sqrt{0.000441}

  6. Convert the decimal to a fraction.

    0.000441=44110000000.000441 = \frac{441}{1000000}

  7. Find the square root of the numerator and the denominator.

    441=21\sqrt{441} = 21 1000000=1000\sqrt{1000000} = 1000

  8. Calculate the square root of the fraction.

    4411000000=211000\sqrt{\frac{441}{1000000}} = \frac{21}{1000}

  9. Convert the fraction back to a decimal.

    211000=0.021\frac{21}{1000} = 0.021

    The value is 0.021\boxed{\mathbf{0.021}}.

    12) Work out the square root of 0.2809

  10. Convert the decimal to a fraction.

    0.2809=2809100000.2809 = \frac{2809}{10000}

  11. Find the square root of the numerator and the denominator.

    2809=53\sqrt{2809} = 53 10000=100\sqrt{10000} = 100

  12. Calculate the square root of the fraction.

    280910000=53100\sqrt{\frac{2809}{10000}} = \frac{53}{100}

  13. Convert the fraction

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