What exactly IS a square root? - Mathematics Stack Exchange
27 May 2025 at 6:13pm
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 ...
What does the small number on top of the square root symbol mean?
31 May 2025 at 1:33am
$\begingroup$ 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.
Derivative of square root - Mathematics Stack Exchange
30 May 2025 at 10:05pm
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.
complex numbers - What is $\sqrt {i}$? - Mathematics Stack Exchange
30 May 2025 at 11:00am
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
Why is the square root of a negative number impossible?
29 May 2025 at 6:39pm
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 ...
Is the square root of a negative number defined?
29 May 2025 at 1:02pm
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.
Approximating square roots using binomial expansion.
30 May 2025 at 2:39am
In fact you can take any two numbers which can be added to get 2 (not nesserly 0.01 but at least you should know the root of one of them So for example $\sqrt{2} = {(1+1)^{1/2}}$ Know all what you need is to expand it using bio theorem and for 2 terms you ll get 1.5
why the square root of x equals x to the one half power
26 May 2025 at 4:59am
Law of Exponents $\,\Rightarrow\,x = a^{1/2}\,$ is a positive root of $\, x^2 - a,\ $ assuming $\ a > 0.$ Further, by definition, $\,\sqrt{a}\ $ is also a positive root of $\, x^2 - a.$ If $\ a^{1/2}\neq \sqrt{a}\ $ then the quadratic $\,x^2-a\,$ has $> 2$ roots: $\,a^{1/2},\ {\pm}\sqrt{a},\,$ contradicting the theorem that a nonzero polynomial ...
radicals - How do I get the square root of a complex number ...
27 May 2025 at 10:13am
For instance, the distance formula in any finite number of dimensions is a positive square root - namely, for two points, the distance apart is the square root of the sum of the squares of the respective differences of coordinates.
Why can't you square both sides of an equation?
29 May 2025 at 3:33pm
There is nothing wrong with taking the square of both sides of an equation. However, you have to be careful if you want to take the square root of both sides, because the square root is not a normal function: it has two values $\pm \sqrt x$. By convention, the positive square root is chosen, and that is what people mean when they say "the ...
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
27 May 2025 at 6:13pm
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 ...
What does the small number on top of the square root symbol mean?
31 May 2025 at 1:33am
$\begingroup$ 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.
Derivative of square root - Mathematics Stack Exchange
30 May 2025 at 10:05pm
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.
complex numbers - What is $\sqrt {i}$? - Mathematics Stack Exchange
30 May 2025 at 11:00am
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
Why is the square root of a negative number impossible?
29 May 2025 at 6:39pm
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 ...
Is the square root of a negative number defined?
29 May 2025 at 1:02pm
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.
Approximating square roots using binomial expansion.
30 May 2025 at 2:39am
In fact you can take any two numbers which can be added to get 2 (not nesserly 0.01 but at least you should know the root of one of them So for example $\sqrt{2} = {(1+1)^{1/2}}$ Know all what you need is to expand it using bio theorem and for 2 terms you ll get 1.5
why the square root of x equals x to the one half power
26 May 2025 at 4:59am
Law of Exponents $\,\Rightarrow\,x = a^{1/2}\,$ is a positive root of $\, x^2 - a,\ $ assuming $\ a > 0.$ Further, by definition, $\,\sqrt{a}\ $ is also a positive root of $\, x^2 - a.$ If $\ a^{1/2}\neq \sqrt{a}\ $ then the quadratic $\,x^2-a\,$ has $> 2$ roots: $\,a^{1/2},\ {\pm}\sqrt{a},\,$ contradicting the theorem that a nonzero polynomial ...
radicals - How do I get the square root of a complex number ...
27 May 2025 at 10:13am
For instance, the distance formula in any finite number of dimensions is a positive square root - namely, for two points, the distance apart is the square root of the sum of the squares of the respective differences of coordinates.
Why can't you square both sides of an equation?
29 May 2025 at 3:33pm
There is nothing wrong with taking the square of both sides of an equation. However, you have to be careful if you want to take the square root of both sides, because the square root is not a normal function: it has two values $\pm \sqrt x$. By convention, the positive square root is chosen, and that is what people mean when they say "the ...
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
