Difference between revisions of "Square root"
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| − | + | A '''square root''' of a number ''x'' is a number ''y'' such that <math>y^2 = x</math>. Thus ''y'' is a square root of ''x'' if and only if ''x'' is the square of ''y''. The square root of a number ''x'' is denoted <math>\sqrt x</math>. For instance, <math>\sqrt 4 = 2<\math>. When we consider only [[positive]] [[real number|reals]], the square root function is the [[inverse]] of the squaring function. However, this does not hold more generally because every positive real has two square roots, one positive and one negative. The notation <math>\sqrt x</math> is used for the positive square root. | |
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| + | It is also written as the one half exponent of the argument, so that squaring ''undoes'' this function just a multiplying by 2 undoes <math>\frac12</math>. Similar function can be generalized to any real number power as well as even [[complex]] powers! | ||
Revision as of 18:46, 6 July 2006
A square root of a number x is a number y such that 
. Thus y is a square root of x if and only if x is the square of y. The square root of a number x is denoted 
. For instance, $\sqrt 4 = 2<\math>. When we consider only [[positive]] [[real number|reals]], the square root function is the [[inverse]] of the squaring function. However, this does not hold more generally because every positive real has two square roots, one positive and one negative. The notation <math>\sqrt x$ (Error compiling LaTeX. Unknown error_msg) is used for the positive square root.
It is also written as the one half exponent of the argument, so that squaring undoes this function just a multiplying by 2 undoes 
. Similar function can be generalized to any real number power as well as even complex powers!
