Ask Me Help Desk

Ask Me Help Desk (https://www.askmehelpdesk.com/forum.php)
-   Mathematics (https://www.askmehelpdesk.com/forumdisplay.php?f=199)
-   -   How to you find the square root of a number? (https://www.askmehelpdesk.com/showthread.php?t=388593)

  • Aug 19, 2009, 03:33 PM
    baker44
    How to you find the square root of a number?
    It's been several years since high school. How to you find the square root of a number?
  • Aug 19, 2009, 04:28 PM
    HelpinHere

    Why exactly do you need this?

    Virtually all calculators produced today have a square root function. Just use that.
    If you aren't allowed to use a calculator for whatever reason, you can always use the guess and check method.
    i.e. starting with, say, 45. You know that 6^2=36, and 7^2=49, so you can reasonably guess that the square root of 45 is ~6.7
    Or, you can do it the LONG way...
    It's too lenghty to type out here (for me at least, :p) so I'll just link you a good explaination:
    How to manually find a square root
  • Aug 19, 2009, 05:24 PM
    galactus
    Here is an iterative method I prefer if I have to do these by hand. It is called the Babylonian method.

    Say we want the square root of 14,

    Make a guess for the first iteration. We know that it is going to be between 3 and 4, because 3^2=9 and 4^2=16.

    The formula is

    where S is the number we are finding the square root of.

    Let's make a guess of



    Next iteration:



    Next iteration:



    Compare to

    It only took 3 iterations to get it accurate to within about 10 decimals places.

    The better the initial guess, the faster it will converge. You can even start with a bad guess and it will converge, though not as fast.
  • Aug 20, 2009, 12:53 AM
    Unknown008

    I'll explain how the formula is good, if you allow me.

    You want to know:



    Let x be the square root.

    Then, square both sides:



    Since it's an equation, you can add x^2 on both sides:





    Now divide by 2x;







  • Oct 25, 2010, 10:51 PM
    ROLCAM
    The square root of a number =

    Say the square root of :-1234567890.=35136 See the workings below.
    This is very hard to portray on this medium. The trick is the side figures are multuplied by 2. e.g 35*2=70, 351*2 = 702
    3513*2 = 7026

    3 5 1 3 6
    /12,34,56,78,90
    3 9
    ---------------------------------
    3,34
    65 3,25
    --------------------------------
    9,56
    701 7,01
    ------------------------------
    2,55,78
    7023 2,10,69
    --------------------------------------
    45,09,90
    70236 42,14,16
    -----------------------------------------
    2,95,74
    ========================

    The square root of 12,34,56,78,90 os apprximately 35136.


  • Oct 25, 2010, 11:08 PM
    Unknown008

    Yes, maybe you could try using the [code] tabs so that the spaces are kept and that it becomes easier to understand.

    Like this:

    Code:

              3  5  1  3  6
            /12,34,56,78,90
        3      9
    ------------------------
              3,34
        65    3,25
    ------------------------
                  9,56
        701      7,01
    ------------------------
                  2,55,78
        7023      2,10,69
    ------------------------
                    45,09,90
        70236      42,14,16
    ------------------------
                    2,95,74
    ========================

    But I'm not sure if the spacings are good... =/ You might want you re-adjust them.

  • All times are GMT -7. The time now is 07:50 AM.