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What exactly IS a square root? - Mathematics Stack Exchange
It's come to my attention that I don't actually understand what a square root really is (the operation). The only way I know of to take square roots (or nth root, for that matter) it to know the an...
Square roots -- positive and negative - Mathematics Stack Exchange
For convenience, the square root of non-negative real numbers is usually taken to be the non-negative real value, but there is nothing other than practicality to stop you from taking some other pattern. Such arbitrary choices can raise significant issues when considering, for example, cube-root functions defined on the real and complex numbers.
What is $\sqrt {i}$? - Mathematics Stack Exchange
The square root of i is (1 + i)/sqrt (2). [Try it out my multiplying it by itself.] It has no special notation beyond other complex numbers; in my discipline, at least, it comes up about half as often as the square root of 2 does --- that is, it isn't rare, but it arises only because of our prejudice for things which can be expressed using small integers.
Why is square root symbol the principal square root?
When researching square roots I found that $\\sqrt{x}$ is the principal square root and $\\pm\\sqrt{x}$ is the square roots, with the reason for why being given through an example equation by user9464...
What is a square root? - Mathematics Stack Exchange
Powers are multiplying a value by itself. What is a square root? To be clear, I'm asking what function a square root actually performs? I can't seem to come up with an answer without the concept of powers to refer to. For example; how would you go about solving the square root of $121$ without prior knowledge that $11^2$ is $121$?
Why is the square root of a negative number impossible?
It is impossible to find the square root of negative one, or the square root of any negative number, because no number times itself can equal a negative number.
Square root inside a square root - Mathematics Stack Exchange
Square root inside a square root Ask Question Asked 11 years, 9 months ago Modified 5 years, 3 months ago
Derivative of square root - Mathematics Stack Exchange
What would be the derivative of square roots? For example if I have $2 \\sqrt{x}$ or $\\sqrt{x}$. I'm unsure how to find the derivative of these and include them especially in something like implicit.
functions - Square root definition - Mathematics Stack Exchange
It is standard when working over the real numbers to take the square root function to return the non-negative square root. This is called the principal square root and is described in the Wikipedia page you refer to.
Why can't you square both sides of an equation?
A slightly higher-level way to phrase the issue is that the usual square root is not a "function" at all. "Doing the same thing" to both sides only preserves equality if "doing the same thing" means "apply a function." The square root (allowing both positive and negative roots) is a multivalued map, so it need not preserve the relation of equality.
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