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Topic: Sqrt(15) proof by prime factors
Replies: 1   Last Post: Oct 20, 2009 1:28 AM

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 Jerry Johnson Posts: 5 Registered: 10/20/09
Re: Sqrt(15) proof by prime factors
Posted: Oct 20, 2009 1:28 AM

Rethink your original claim...For example, we know that sqrt(2) is
irrational, and by your claim, sqrt(2) = sqrt(1)+sqrt(1). But sqrt(1) = 1,
making sqrt(1) rational, which would imply that sqrt(2) is rational as well.
So, as a start, review (i.e. reflect on) the properties of taking square
roots. Once you have that correct, you can plan a solution path...

----- Original Message -----
From: "Morbine" <discussions@mathforum.org>
To: <discretemath@mathforum.org>
Sent: Monday, October 19, 2009 9:05 PM
Subject: Sqrt(15) proof by prime factors

> Having difficulty figuring out where to start on this question. The exact
> question is this:
>
> Prove by considering prime factors that sqrt(15) is irrational.
>
> sqrt(15) = sqrt(3) + sqrt(5), correct? So then I can prove that sqrt(3)
> and sqrt(5) are both irrational but then how does that prove that sqrt(15)
> is also irrational?
>
>

Date Subject Author
10/20/09 Morbine
10/20/09 Jerry Johnson