1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Help with an aproximation

  1. Nov 5, 2012 #1
    I need to show that: [itex] sqrt(x^2 - l^2) - l ≈ {x^2}/{2l} [/itex]

    2. That should be valid for x << l

    3. First I've tried to isolate l in the sqrt, but it got me nowhere. Anyone could show me a simple way to solve this?
  2. jcsd
  3. Nov 5, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    If [itex]x<<\ell\,,\ [/itex] then [itex]\sqrt{x^2 - \ell^2}\ [/itex] is undefined.

    Did you mean [itex]\sqrt{\ell^2-x^2}\ ?[/itex]
  4. Nov 5, 2012 #3
    Sorry, I mean [itex]\sqrt{\ell^2+x^2}\ [/itex]
  5. Nov 5, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper

    Multiply sqrt(l^2+x^2)-l by (sqrt(l^2+x^2)+l)/(sqrt(l^2+x^2)+l) (which is 1) and reduce the algebra. Think about what that is approximately equal to if x<<l.
  6. Nov 6, 2012 #5
    Got it.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook