How many irrational numbers are there between 1 and 6 ?

F. 1
G. 3
H. 4
J. 10
K. Infinitely many

Question

How many irrational numbers are there between 1 and 6 ?

    F.   1
    G.   3
    H.   4
    J. 10
    K. Infinitely many

directrix · Answer

There are infinitely many non-imaginary numbers between 1 and 6 or between any two numbers for that matter.

To see how this works, pick any two of those infinitely many numbers between 1 and 6, multiply them, and then take the square root provided the radicand is not a perfect square.

The result will be an irrational number.

Example:

7/4 and 9/4

7/4  * 9/4  = 63 / 16

The square root of 63/16 =  ( 3* sqrt(7) all over 4 ). This is an irrational number.

You can generate as many of these as you like.  @tosin

Therefore,   K. Infinitely many