Rational Numbers and Square Roots

Date: 10/07/98 at 18:55:40
From: Will Chase
Subject: Rational numbers and square roots

Our teacher told us to find all the rational numbers we could 
containing a sqrt symbol. To do this I could only think of sqrt4, 
sqrt9, sqrt16, sqrt25, etc. Are there other things that could go 
under the sqrt symbol that would be considered rational?

Date: 10/08/98 at 12:23:12
From: Doctor Peterson
Subject: Re: Rational numbers and square roots

Hi, Will - 

How about 1/4, for example? Try squaring any rational number, and put 
it under a sqrt!

Of course, I hope you recognize that numbers don't contain sqrts - 
only representations of numbers do! Any rational number that can be 
written with a sqrt can also be written without one; that's the 
definition of rational. 

So your sqrt(4) is really 2, and doesn't need any sqrt.

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