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rv this edit: "(square root function is single-valued)" replacing +/- symbolism
All numbers have two square roots, one positive and the other negative:
All numbers have two square roots, one positive and the other negative:
:<math>3 \cdot 3 = 9</math> and <math>-3 \cdot -3 = 9</math>
:<math>3 \cdot 3 = 9</math> and <math>-3 \cdot -3 = 9</math>
As such, the technically correct way of writing is
:<math>\sqrt{9} = \pm 3</math>
When speaking of "''the'' square root of ''x''", people usually refer to the positive square root. For example:
When speaking of "''the'' square root of ''x''", people usually refer to the positive square root. For example:
:<math>\sqrt{9} = 3</math>
:<math>\sqrt{9} = 3</math>
:<math>\sqrt{-1} = i</math> which for example leads to <math>\sqrt{-9} = 3i</math>
:<math>\sqrt{-1} = i</math> which for example leads to <math>\sqrt{-9} = 3i</math>
The statements in [[#Two square roots for each number|"Two square roots for each number"]] also apply to negative numbers.
The statements in [[#Two square roots for each number|"Two square roots for each number"]] also apply to negative numbers. Thus the technically correct way of writing the above example would be:
:<math>\sqrt{-9} = \pm 3i</math>
==Alternate expressions and notations==
==Alternate expressions and notations==