Posted by anoynomous on Tuesday, April 9, 2013 at 7:51am.
find two irrational numbers between 2.5 and 4.5

maths rational no.  Steve, Tuesday, April 9, 2013 at 11:21am
2.5 = 5/2
4.5 = 9/2
so, a short list of rational numbers between the two might contain
6/2 7/2 8/2
Expressing them as 6ths,
2.5 = 15/6
4.5 = 27/6
Now there are a lot more possibilities, all multiples of 1/6

maths rational no.  Steve, Tuesday, April 9, 2013 at 11:25am
Oops! I missed the "irrational" part!
Since
2.5^2 = 6.25
4.5^2 = 20.25
Pick any integers between those, except 9 and 16, which are perfect squares.
√7 √8 √10 ... √20
are all irrational.
Since
2.5^3 = 15.625
4.5^3 = 91.125
There are lots of possibilities there, excluding 27 and 64:
∛16 ∛17 ... ∛91
are all irrational
You can pick noninteger values, as long as they don't turn out to be perfect powers.
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