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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 ...
Why is square root symbol the principal square root?
2 When researching square roots I found that x−−√ x is the principal square root and ± x−−√ ± x is the square roots, with the reason for why being given through an example equation by user9464 of: What is the positive real number x x such that x2 =π x 2 = π?
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.
Is the square root of a negative number defined?
A square root of a number a a is any number x x with x2 = a x 2 = a, or equivalently a root of the polynomial x2 − a x 2 a. The fundamental theorem of algebra implies that every complex number a a has a square root.
Square root of zero - Mathematics Stack Exchange
I'm old $35$ but starting just now with maths, so sorry if I ask non complex questions. $0$ is the only number that just has one square root. Is the explanations for this simply that 0 in arithmeti...
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
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.
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.
Square root inside a square root - Mathematics Stack Exchange
Square root inside a square root Ask Question Asked 11 years, 7 months ago Modified 5 years ago
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.
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