Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Square Root Trick


Date: 08/13/97 at 13:09:50
From: Daniel Lee
Subject: Square root

Is there a formula to calculate sqrt(x+sqrt(x+sqrt(x+... ? 


Date: 08/18/97 at 14:40:13
From: Doctor Rob
Subject: Re: Square root

Yes, there is a very cute trick to figure this out.

If x = 0, presumably this value is 0.  If x < 0, I'm not sure that
this makes sense, but perhaps even so.  We assume x > 0.  

Let a = sqrt(x+sqrt(x+sqrt(x+...))).  Then square and subtract x.  
You get

    a^2 - x = sqrt(x+sqrt(x+...))
            = a

This is a quadratic equation for a. When you solve it for a, you
get two solutions. You must reject one of them as extraneous. That
leaves you with the formula you seek.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Exponents

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/