Saturday

October 25, 2014

October 25, 2014

Posted by **Lauren** on Saturday, February 26, 2011 at 1:55pm.

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 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 -
**Reiny**, Saturday, February 26, 2011 at 2:59pmfor √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

**Answer this Question**

**Related Questions**

Math - What are irrational, rational, and natural numbers? A rational number is ...

very EASY Math terms Defintions - Please help someone!!!! a number that can be ...

Algebra - If a number is not a rational number then it is a? 1.an integer 2.an ...

Math term definitions - Please help someone!!!! a number that can be expressed ...

math - Take any number (except for 1). Square that number and then subtract one...

Math ms sue help - please help me with these defintions of math terms please: a ...

Algebra - If a number is not a rational number then it is a? 1.an integer 2.an ...

math - 1. Which of the following numbers is an example of an integer? a. -15 b. ...

math - could someone please help me with this problem. Which of the following ...

Math Definitions - a number that can be expressed as the product of 3 equal ...