Square Root

Understanding square root requires examining multiple perspectives and considerations. - 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. What exactly IS a square root? 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... Is the square root of a negative number defined?. This approach is not without fault either, since you're now no longer talking strictly about the square root of a complex number. The points on the Riemann surface tell you which square root to pick, and there is one point for each square root.

Since -1 is a complex number, not a point on the surface, $\sqrt {-1}$ doesn't make sense. What does the small number on top of the square root symbol mean?. Ask Question Asked 12 years, 3 months ago Modified 5 years, 2 months ago

radicals - How do I get the square root of a complex number .... The square root is not a well defined function on complex numbers. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number. Another key aspect involves, powers are multiplying a value by itself. 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 $121$? Derivative of square root - Mathematics Stack Exchange. Building on this, 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. Where and when is $\sqrt {0}$ defined? The square root was defined long before some people hopped around a Christmas tree with a drum, and that definition works perfectly well with $0$, no matter if real or complex. Can the square root of a real number be negative?

Dealing with the questions of functions in eleventh class my maths teacher says that square root of a real number is always positive. From another angle, 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.