Difference between revisions of "Square root"
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| − | + | The '''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 number|positive]] [[real number|reals]], the square root function is the [[Function/Introduction#The_Inverse_of_a_Function|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, or principal, square root. | |
| − | It is also written as the one half exponent of the argument, so that squaring ''undoes'' this function just | + | It is also written as the one half exponent of the argument, so that squaring ''undoes'' this function, just as multiplying by 2 undoes <math>\frac12</math>. Similar functions can be generalized to any real number power, as well as [[complex number|complex]] powers. |
== See also == | == See also == | ||
* [[Algebra]] | * [[Algebra]] | ||
* [[Exponent]]s | * [[Exponent]]s | ||
Revision as of 03:21, 30 October 2006
The 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, or principal, square root.
It is also written as the one half exponent of the argument, so that squaring undoes this function, just as multiplying by 2 undoes 
. Similar functions can be generalized to any real number power, as well as complex powers.
