How do you find square roots-?

Answer 1

In order to find square root, you must take the number you are working with, and find a number that can multiply by itself to get to that number.

Example: To find the square root of 100, you would take 10*10. That will give you the number, 100.

Example 2: An easy number is 49. The square root of 49 is 7. 7*7 is 49.

Answer 2

This is something best left to a calculator.One way to do it manually is to try out different numbers; say you want the square root of 2, then, for example:

* 1 squared is 1, which is less than 2

* 2 squared is 4, which is more than 2

Therefore, the actual square root is somewhere between 1 and 2. You can repeat this with decimals, for example 1.5 squared is 2.25 - this is too much, so now the square root is between 1 and 1.5.

More efficient methods exist as well, but all of them are iterative, meaning you need to iterate (repeat) a series of steps several times, until you get the desired accuracy.

Answer 3

One 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 kkk, define f(x) = x^2 – kkk. Then finding the square root of kkk 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, … 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 you want the square root of 7 and you you start with x0 = 5 (a pretty poor choice since 5^2 is 25, which is nowhere near 7).
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.

Answer 4

The product of two numbers of the same number is the square root of that number as for example 5 times 5 = 25 and so its square root is 5.

Or else use a calulator.