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What exactly IS a square root? - Mathematics Stack Exchange
The definition of "the square root of x x " is "the positive number y y such that y2 y 2 equals x x ". This is an implicit definition, and so it makes sense that it takes a little thought as to how to actually compute it (Trevor Wilson's link is a good one). But as Paul Picard said, don't let the notation x1/2 x 1 / 2 (or similarly xπ x π) fool you into thinking that you're multiplying x x ...
What is $\\sqrt{i}$? - Mathematics Stack Exchange
The square root of i is (1 + i)/sqrt (2). [Try it out my multiplying it by itself.] It has no special notation beyond other complex numbers; in my discipline, at least, it comes up about half as often as the square root of 2 does --- that is, it isn't rare, but it arises only because of our prejudice for things which can be expressed using small integers.
What is a square root? - Mathematics Stack Exchange
Powers are multiplying a value by itself. What is a square root? To be clear, I'm asking what function a square root actually performs? I can't seem to come up with an answer without the concept of powers to refer to. For example; how would you go about solving the square root of 121 121 without prior knowledge that 112 11 2 is 121 121?
radicals - How do I get the square root of a complex number ...
The square root is not a well defined function on complex numbers. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number.
Whats the rule for putting up a plus-minus sign when taking under root?
But when we take the square root of the left hand side, we must also arrive at a positive number (by definition). In this simple example, we can easily see that a -7 value for x would also satisfies the original equation, so we have to apply a negative to that -7 in order to arrive at the positive (again, by definition) square root.
What does the small number on top of the square root symbol mean?
What does the small number on top of the square root symbol mean? Ask Question Asked 12 years, 5 months ago Modified 5 years, 4 months ago
Why is the square root of a negative number impossible?
It is impossible to find the square root of negative one, or the square root of any negative number, because no number times itself can equal a negative number.
Why the name "square root"? - Mathematics Stack Exchange
The idea of the square root existed in Egypt and the technical term for it was Knbt, literally “corner” or “angle.” Peet has the explanation for that, that the length of each of the two sides of a square containing any corner of it was its square root.
Find the square root of a matrix - Mathematics Stack Exchange
The matrix is symmetric, so it is certainly diagonalizable. Trace and determinant are both positive, so both eigenvalues are positive. So if you can diagonalize, the diagonal form will have a square root, QAQ−1 = D =P2 Q A Q 1 = D = P 2, where Q Q is the change-of-basis matrix. That means that A =Q−1P2Q = (Q−1PQ)2 A = Q 1 P 2 Q = (Q 1 P Q) 2, so you can let B = Q−1PQ B = Q 1 P Q. So ...
algebra precalculus - Why is $\sqrt {a^2+b^2}\neq a+b$, and is there ...
You are trying distribute exponents across addition, but exponentiation is not distributive across addition 2. As an aside a square root is an exponentiation to a 1 2 1 2 power (x−−√ =x1 2 x = x 1 2) You are probably used to distributing multiplicands, which is valid as multiplication is distributive across addition.
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