Posted by Lauren on Saturday, February 26, 2011 at 1:55pm.
x is a number between 3 and 50.
How many vales of x is radical x / 13 a rational number?

Math  MathMate, Saturday, February 26, 2011 at 2:57pm
"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 noninteger 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  Reiny, Saturday, February 26, 2011 at 2:59pm
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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