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/