2019年8月1日 · Square roots of real numbers can be negative. -4 is a square root of 16. But remember: $\sqrt{x}$ means the $\mathit{principal}$ square root of x, not just the square root of x. You would be correct to say, "the principal square root of a real number cannot be negative"

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.

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.

The ambiguity in the answer lies not with the square root... but rather on the negative sign. The value $-5^2$ is most commonly interpreted as $-(5^2)$ which simplifies as $-25$ . It is distinctly different than the value $(-5)^2$ which simplifies as $25$ .

2020年2月8日 · The square root function, like all bona fide functions, is single-valued rather than multi-valued, so if we were tasked with creating our own square root function from scratch we would have to make a choice between the two square roots of every positive number as the value the function takes; if we want to further impose continuity (and ...

2014年5月27日 · 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.

(And "negative square root" isn't exactly the right term. It would be a square root of a negative number. What's negative is not the square root, but something else.)

2018年6月8日 · What I know. If I'm not mistaken: $\pm \sqrt{\frac{x}{y}}=\frac{\pm \sqrt{x}}{\pm \sqrt{y}}$ a repeated $\pm$ sign in an equation means make every "$\pm$" sign a plus or make every one of them a minus(you can't take one as a positive and the other as a negative, then $\mp$ sign would be useless[e.i. $\pm 3 \cdot \pm 4 = 3\cdot 4 \,\,\,\,\, \text{ or } \,\, (-3) \cdot ( …

2021年8月23日 · Why non-real means only the square root of negative? 3. square root of $\frac{2+\sqrt{3}}{4}$ 2.

2015年6月4日 · Here, the square root of D is done by simply square rooting the diagonal eigenvalues. The square root of the inverse of P is obtained by replacing the square root of the eigenvalues by their inverse values. This is diagonalization. $\endgroup$ –