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April 20, 2014

April 20, 2014

Posted by **anoynomous** on Tuesday, April 9, 2013 at 7:51am.

- maths- rational no. -
**Steve**, Tuesday, April 9, 2013 at 11:21am2.5 = 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 11:25amOops! 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 non-integer values, as long as they don't turn out to be perfect powers.

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