Finding Square Root
Finding square root of a number that I don't know was a pain for me.
Using that long division method 😭.
Like 841 it's the square root of 29, I didn't know that I tried many ways to over come but in the end I just used the calculator.
I was furious and curious can I find the square value of any number using (a+b)² expression then maybe I can also find the square root of perfect square numbers using it?
I came up with (10a+b)²= S [I know it's looks similar to that expression and actually it is I'm not claiming I found something new I just got rid of my problem]
100a²+20ab+b² = S (s is the targeted square value of which square root we are looking for.)
Now conditions; a= or < S, b can be only a single digit from 0 to 9.
Example: S=144.
100a²+20ab+b² =144
Then a=1 => 100+20b+b²=144
20b+b²=44
(For selecting b we can guess the number or just divide remaining number by 20a [a=1 in this case].)
44/20 ≈2
Now substituting as a test-
20(2)+(2)² =44
LHS = RHS then
a=1, b=2
(10×1+2)² =12².
I will do further case study related to this stuff.