How do you find sqaure root?

Answer 1

Divide the number by itself (a number squared is a number multiplied by itself)... next time click on spell check.

* * * * *

That is pure drivel. Any number (other than zero) divided by itself, gives 1. Not a particularly useful answer!. See the expert answer, which makes a bit more sense.

Answer 2

One way is to bracket estimates.Suppose you want to find the square root of 5.

2^2 = 4 < 5 , 9 = 3^2 so that 2 < sqrt(5) < 3

Next 22^2 = 484 < 500 < 529 = 2.3^2 so that 2.2 < sqrt(5.00) < 2.3

Next 223^2 = 49729 < 50000 < 50176 = 224^2 and so 2.23 < sqrt(5) < 2.24

and so on. In time, you will get to an answer with a satisfactory degree of accuracy. Remember that most square roots (in real life) are Irrational Numbers and so you will only be able to get an approxi,ate answer.

Also, remember that the number in the middle (5, 500, 50000) gets multiplied by 100 each time.

Another way to estimate the square root of a number is by iteration. This entails making a guess at the answer and then improving on it. Repeating the procedure should lead to a better estimate at each stage. One such is the Newton-Raphson method.If you want to find the square root of a number k, define f(x) = x^2 - k.
Then finding the square root of k is equivalent to solving f(x) = 0.

Let f'(x) = 2x. This is the derivative of f(x) but you do not need to know that to use the N-R method.

Start with x0 as the first guess. Then let xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, 3 ... Provided you made a reasonable choice for the starting point, the iteration will very quickly converge to the true answer.

It works even if your first guess is not so good:

Suppose k = 5: that is, you want to find the square root of 5, and you start with x0 = 5 (a pretty poor choice since 5^2 is 25, which is nowhere near 5).
Even so, x3 = 2.2362512515, which is less than 0.01% from the true value. Finally, remember that the negative value is also a square root.