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March 24, 2017

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x is a number between 3 and 50.
How many vales of x is radical x / 13 a rational number?

  • Math - ,

    "x is a number between 3 and 50." requires any number x (integer, fractional or decimal) between the given limits such that √(x/13) is rational.

    The number of integers is limited to 1, namely 13, since √(13/13)=1 is rational. Multiplying 13 by the nearest perfect square exceeds the upper limit.

    However, there are many non-integer rational numbers that fit the bill.

    Basically, we multiply 13 by fractions whose numerator and denominator are perfect squares.

    13/4
    13*4/9
    13*9/4
    13*25/9
    13*9/25
    13*25/36
    13*36/25
    13*36/49
    13*49/36
    13*49/64
    13*64/49
    ...
    As you can see, the list can go on and on, and the list is long, if not infinite.

    You may want to double check if the question actually meant:
    "x is an integer between 3 and 50."

  • Math - ,

    for √x/13 to be rational, x must be a perfect square.

    perfect squares between 3 and 50 are

    4,9,16,25,36, and 49

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