24 (notice I broke the pattern root finding tend to be heuristic)2.24^2 = 5.0176which is close enough for mebut I sense you want more.we know the number has to be smaller than 2.24 but not too much smallerlets try 2.2372.......
find the midpoint between 2 and 2.25
2.125 2.125^2 is 4.515625 yuck thats worse
so try 2.24 (notice I broke the pattern root finding tend to be heuristic)
2.24^2 = 5.0176
which is close enough for me
but I sense you want more.
we know the number has to be smaller than 2.24 but not too much smaller
lets try 2.237
2.237^2 = 5.004169
you could keep going forever but you will only add more significant figures.
it turns out your calculator does it in much the same way.
to find the square root of a number without a calculator, many will learn the process once they take calculus.
if you want to read up on one of the easiest methods of doing it (imo) you can look here: http://en.wikipedia.org/wiki/Newton%27s_…
if you havent taken calculus yet, this may seem confusing, but i will do it anyway
so using the method above ^ the square root of 5 can be obtained by first making a guess of what the answer is. I will use 1 as my guess
x1= 1 - (1^2 - 5) / (2*1) = 3
x2 = 3 - (3^2 - 5) / (2*3) = 2.33333333
x3 = 2.33333333 - (2.33333333^2 - 5) / (2* 2.33333333) = 2.23809524
x4 = 2.23809524 - (2.23809524^2 - 5) / (2* 2.23809524) = 2.2360689
^ so as you can see, the answer gets really close to 2.236, and thats how you find the square root without a calculator
you can always do a guess and check by multiplying two same numbers together...
the official formula is for advanced college math, you can look here:
http://en.wikipedia.org/wiki/Methods_of_…
This link should help with the "long hand" method of finding the square root of a number. Good luck and I hope this helps!
http://www.homeschoolmath.net/teaching/s…
