2015年9月20日 · The principal square root of minus one is i. It has another square root -i. I really dislike the expression "the square root of minus one". Like all non-zero numbers, -1 has two square roots, which we call i and -i. If x is a Real number then x^2 >= 0, so we need to look beyond the Real numbers to find a square root of -1. Complex numbers can be thought of as …

2015年5月12日 · Since it's continuous, the square root of any positive real number is always a well-defined positive real number: Given the positive gap-between-rationals which you want to take the square root of, the square root is the positive gap-between-rationals such that any rational greater than the square-root-gap squares to a rational greater than the ...

The suaqre root of a (non-negative) real number is non-negative by definition, but is there a similar decision for "the" square root of other (complex) numbers? $\endgroup$ – Wolfgang Kais Commented Jul 8, 2023 at 17:59

The general guideline of writing the square root as a fractional power and then using the power and chain rule appropriately should be fine however. Also, remember that you can simply pull out a constant when dealing with derivatives - see below.

2019年11月19日 · $\begingroup$ Minor point: I notice quite a few elementary algebra books as well as some writers here taking the view that the n-th root of x is defined as x to the power 1/n. I disagree strongly. I disagree strongly.

2014年6月24日 · The square root of the square root of x is therefore $$\sqrt{\sqrt x} = (\sqrt x)^{1/2} = (x^{1/2})^{1/2} ...

Now, let's explore how to translate a square root function vertically. y = #sqrt(x) + 3# or y = #sqrt(x) - 4#. The addition or subtraction on the OUTSIDE of the square root function will cause the graph to translate up or down. Adding 3 will raise the graph up, and subtracting 4 will lower the graph by 4 units. (see graph)

2015年9月10日 · There is no Real number whose square is -16. The principal Complex square root sqrt(-16) = 4i -4i is also a square root of -16 If a in RR then a^2 >= 0. So there is no Real square root of -16. If i is the imaginary unit, then i^2 = -1 and we find that: (4i)^2 = 4^2*i^2 = 16 * -1 = -16 So 4i is a square root of -16.

2015年9月8日 · 361 = 19^2, so sqrt(361) = 19. See explanation for a few methods... Prime Factorisation One of the best ways to attempt to find the square root of a whole number is to factor it into primes and identify pairs of identical factors. This is a bit tedious in the case of 361 as we shall see: Let's try each prime in turn: 2 : No: 361 is not even. 3 : No: The sum of the digits …

2014年4月13日 · Square root is defined exactly as much for the real numbers as for the complex numbers. There are two square roots of four, namely ${-2, 2}$ and there are two square roots of $-1$, namely ${-i, i}$. It is irrationally inconsistent to accept that there is a defined square root over the non-negative real number line, but not elsewhere.