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< | + | 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. |
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! | 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 18:47, 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, 
. When we consider only positive 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 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!
