complex numbers - What is $\sqrt{i}$? - Mathematics Stack Exchange
30 Nov 2024 at 9:05am
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
What is the square root of negative one? + Example - Socratic
28 Nov 2024 at 11:05pm
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 an extension of Real numbers from ...
What exactly IS a square root? - Mathematics Stack Exchange
25 Nov 2024 at 10:51am
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 ...
algebra precalculus - Square root inside a square root - Mathematics ...
29 Nov 2024 at 7:47am
The square root of the square root of x is therefore $$\sqrt{\sqrt x} = (\sqrt x)^{1/2} = (x^{1/2})^{1/2} ...
Derivative of square root - Mathematics Stack Exchange
29 Nov 2024 at 8:05pm
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.
Whats the rule for putting up a plus-minus sign when taking under root?
27 Nov 2024 at 4:22am
You could say "the square roots of $49$ are $\pm 7$" and that would be fine; but otherwise saying "the square root of $49$" usually refers to what we write as $\sqrt{49}$. The $\sqrt{\ }$ symbol always refers to the positive root by default, so although $\sqrt{49}=7$ (which is positive) is 'the square root of $49$', $-\sqrt{49}=-7$ is another ...
linear algebra - Square root of Positive Definite Matrix - Mathematics ...
28 Nov 2024 at 6:26pm
"The unique square root of a positive semidefinite matrix." International Journal of Mathematical Education in Science and Technology 37.8 (2006): 990-99 $\endgroup$ ? David Veitch
What does the small number on top of the square root symbol mean?
28 Nov 2024 at 9:17pm
$\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.
Why is the square root of a negative number impossible?
28 Nov 2024 at 9:25pm
The square root of a negative number is possible! Square definition:"In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2".
Find the square root of a matrix - Mathematics Stack Exchange
27 Nov 2024 at 5:37pm
As traditional known the square root of any number would have two result, its cube root would have three ...
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
30 Nov 2024 at 9:05am
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
What is the square root of negative one? + Example - Socratic
28 Nov 2024 at 11:05pm
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 an extension of Real numbers from ...
What exactly IS a square root? - Mathematics Stack Exchange
25 Nov 2024 at 10:51am
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 ...
algebra precalculus - Square root inside a square root - Mathematics ...
29 Nov 2024 at 7:47am
The square root of the square root of x is therefore $$\sqrt{\sqrt x} = (\sqrt x)^{1/2} = (x^{1/2})^{1/2} ...
Derivative of square root - Mathematics Stack Exchange
29 Nov 2024 at 8:05pm
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.
Whats the rule for putting up a plus-minus sign when taking under root?
27 Nov 2024 at 4:22am
You could say "the square roots of $49$ are $\pm 7$" and that would be fine; but otherwise saying "the square root of $49$" usually refers to what we write as $\sqrt{49}$. The $\sqrt{\ }$ symbol always refers to the positive root by default, so although $\sqrt{49}=7$ (which is positive) is 'the square root of $49$', $-\sqrt{49}=-7$ is another ...
linear algebra - Square root of Positive Definite Matrix - Mathematics ...
28 Nov 2024 at 6:26pm
"The unique square root of a positive semidefinite matrix." International Journal of Mathematical Education in Science and Technology 37.8 (2006): 990-99 $\endgroup$ ? David Veitch
What does the small number on top of the square root symbol mean?
28 Nov 2024 at 9:17pm
$\begingroup$ 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.
Why is the square root of a negative number impossible?
28 Nov 2024 at 9:25pm
The square root of a negative number is possible! Square definition:"In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2".
Find the square root of a matrix - Mathematics Stack Exchange
27 Nov 2024 at 5:37pm
As traditional known the square root of any number would have two result, its cube root would have three ...
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
