Changes

:<math>\sqrt{9} = 3</math>

:<math>\sqrt{9} = 3</math>

When both square roots are to be considered, in mathematics the convention is to use a sign, pronounced "plus or minus" to signify them:

When both square roots are to be considered (usually because variables are involved), in mathematics the convention is to use a sign, pronounced "plus or minus" to signify them:

:<math>\pm \sqrt{9} = \pm 3</math>

:<math>\sqrt{x^2} = \pm x</math>

This has important implications when solving equations, in that, if the square root of both sides is taken, one must be careful to allow for both the positive and negative square root.  A well known example is [[completing the square]] to solve a [[quadratic equation]].

This has important implications when solving equations, in that, if the square root of both sides is taken, one must be careful to allow for both the positive and negative square root.  A well known example is [[completing the square]] to solve a [[quadratic equation]].