You can put this solution on YOUR website! To find a rational number, note that
6.21744 < 6.22000 < 6.22746
and 6.22 can be written 622/100 or reduced to .
EDIT: I had accidentally typed out an extra zero to make 1000 in the denominator. Edited to fix it. Sorry about that.
—
For the irrational number, let's call it x
and x irrational (so x^2 is not an integer)
Now if we restrict our range to:
We can just pick an integer between and (excluding endpoints) and
set to that:
For example, one solution is: is irrational and is approximately 6.2180001, which falls between the limits given. This is just one of many, many solutions.
—
The reason it is irrational is every integer between and , excluding endpoints, can not be a perfect square, and hence its square root is irrational.
