What is the square root of negative one? + Example - Socratic
12 Jan 2025 at 3:16pm
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
12 Jan 2025 at 7:24am
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 ...
complex numbers - What is $\sqrt{i}$? - Mathematics Stack Exchange
14 Jan 2025 at 2:21am
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
Derivative of square root - Mathematics Stack Exchange
13 Jan 2025 at 4:31am
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.
algebra precalculus - Square root inside a square root - Mathematics ...
14 Jan 2025 at 12:05am
The square root of the square root of x is therefore $$\sqrt{\sqrt x} = (\sqrt x)^{1/2} = (x^{1/2})^{1/2} ...
What is a square root? - Mathematics Stack Exchange
13 Jan 2025 at 3:44pm
Hence, we find square root of x is n.So, I would say that square root would be to divide the number x in n equal parts such that each group has value n.This is a relatively simple and qualitative argument.Hope this helps you in understanding.
Whats the rule for putting up a plus-minus sign when taking under root?
13 Jan 2025 at 12:13am
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 ...
What does the small number on top of the square root symbol mean?
14 Jan 2025 at 4:30am
$\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.
Graphs of Square Root Functions - Algebra - Socratic
13 Jan 2025 at 12:42am
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)
What is the square root of -16? - Socratic
9 Jan 2025 at 10:05am
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.
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
12 Jan 2025 at 3:16pm
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
12 Jan 2025 at 7:24am
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 ...
complex numbers - What is $\sqrt{i}$? - Mathematics Stack Exchange
14 Jan 2025 at 2:21am
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
Derivative of square root - Mathematics Stack Exchange
13 Jan 2025 at 4:31am
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.
algebra precalculus - Square root inside a square root - Mathematics ...
14 Jan 2025 at 12:05am
The square root of the square root of x is therefore $$\sqrt{\sqrt x} = (\sqrt x)^{1/2} = (x^{1/2})^{1/2} ...
What is a square root? - Mathematics Stack Exchange
13 Jan 2025 at 3:44pm
Hence, we find square root of x is n.So, I would say that square root would be to divide the number x in n equal parts such that each group has value n.This is a relatively simple and qualitative argument.Hope this helps you in understanding.
Whats the rule for putting up a plus-minus sign when taking under root?
13 Jan 2025 at 12:13am
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 ...
What does the small number on top of the square root symbol mean?
14 Jan 2025 at 4:30am
$\begingroup$ 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.
Graphs of Square Root Functions - Algebra - Socratic
13 Jan 2025 at 12:42am
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)
What is the square root of -16? - Socratic
9 Jan 2025 at 10:05am
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.
WHAT IS THIS? This is an unscreened compilation of results from several search engines. The sites listed are not necessarily recommended by Surfnetkids.com.
