Why isn't there a mathematical formula for finding square root?

Question

Every method for finding square root that I have ever heard always consists of a lot of guesswork and simple math executed in repetition. Mostly, you need to do it intuitively. Why isn't there some sort of formula for finding it? A formula that you could just apply to any number and always come out with the square root?

Like how pi multiplied by the diameter of a circle always equals the circumference(2πr, or πd), and the square length of the hypotenuse of a right triangle is always equal to the square of the lengths of the other two sides(a2 + b2 = c2).

Mathematicians come up with equations for things all the time, why can't we do that with square root. Or is there a formula for finding square root that I have never heard of before?

Either way, I would like to know.

Answer 1

There is a formula, that is how calculators are able to find it easily.



The algorithm is known as Newton's Method. You have to know calculus in order to understand it because it involves derivatives as well as other topics.



http://en.wikipedia.org/wiki/Newton's_method

Answer 2

you need to dig deep to locate the respond. I made a trunk call to a British mathematician and he mentioned it relies upon on what proportion sq. knots are in contact. in line with possibility i'm barking up the incorrect tree and can't see the timber in the process the woodland, yet i think of the respond is the radius of the foliage divided by utilizing pi ne squared. while uncertain continuously hear on your alders fir advice, and spruce up slightly. bear in mind what the acorn mentioned while it grew up. "Geometry." What timber can do is previous beleaf.

Answer 3

facil esta pagina te va a ayudar http://en.wikipedia.org/wiki/Newton's_method