It's been several years since high school. How to you find the square root of a number?
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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:
But I'm not sure if the spacings are good... =/ You might want you re-adjust them.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
========================
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