Showing posts with label algebra. Show all posts
Showing posts with label algebra. Show all posts

Friday, June 1, 2012

Finding the square root of an integer using Calculus

Have you ever been in a situation where you needed to find the square root of an integer (especially imperfect squares), but had no calculator close by? I have. I however remember learning a Calculus trick (in senior high) that has always come to my aid in such situations. Grab a piece of paper and a pen, and come along as I share this trick. The trick requires that you identify some things:
  • The integer (Obviously!)
  • A perfect square that can be got from the integer
  • The remainder in subtracting the perfect square from the integer
The steps involved in deriving the formula for finding the square root of an integer is shown below:

 

As an example, let's find the square root of the integer 7:

PS: You will notice (after a number of practices) that the values got using this method differ slightly from the ones got from the calculator. Do not be alarmed, the values are still correct nonetheless.

I do hope this is helpful and would come in handy when we need it.
Please let me know what your thoughts on any other trick you know. Waiting for your comments. ;-)