# Nested roots

• November 7th 2009, 05:41 AM
shane99
Nested roots
Determine the exact value of √(10 + √(10 + √(10 + ....))) it goes on forever
Show all steps and explain most of them
• November 7th 2009, 07:03 AM
ramiee2010
let $x= \sqrt{10+\sqrt{10+\sqrt{10+......}}}$
therefore
$x= \sqrt{10+x}$
taking square both side
$x^2= (10+x)$
$x^2-x-10=0$
now solve the quadratic equation .........
• November 7th 2009, 12:08 PM
mr fantastic
Quote:

Originally Posted by shane99
Determine the exact value of √(10 + √(10 + √(10 + ....))) it goes on forever
Show all steps and explain most of them

No, that's not how it works. You do not make demands like that. You show what you can do and then say where you're stuck.

I see you've been given a massive start on how to do this question. So now it's your turn. If you need more help, say what you've done and where you get stuck.