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### Irrational Between Two Rationals

```Date: 07/19/2002 at 03:45:17
From: Durga
Subject: Irrational numbers

How can one find two or three irrational numbers between two given
rational numbers, e.g., between 3 and 4?
```

```
Date: 07/19/2002 at 08:16:57
From: Doctor Paul
Subject: Re: Irrational numbers

The square root of a prime number is always irrational.  So look for
a number p such that 3 < sqrt(p) < 4.

Squaring both sides shows that this is equivalent to finding a prime
p such that

9 < p < 16.

It looks like p = 11 and p = 13 will work.

I hope this helps.  Please write back if you'd like to talk about
this some more.

- Doctor Paul, The Math Forum
http://mathforum.org/dr.math/
```
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