It's been several years since high school. How to you find the square root of a number?

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

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.

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;

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.

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.