# Algebra/Square Root is Positive

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## Square Root Is Not Negative

We often say that ${\displaystyle {\sqrt {x}}}$ is the positive number, which when squared is equal to ${\displaystyle x}$. If ${\displaystyle x>0}$ this is perfectly correct, but if ${\displaystyle x=0}$ then ${\displaystyle {\sqrt {x}}={\sqrt {0}}=0}$ which is not positive. So to be technically correct (which is part of the fun of math) we should say that ${\displaystyle {\sqrt {x}}}$ is the non-negative number, which when squared is equal to ${\displaystyle x}$.

If it is needed to express that a square root may be both positive and negative, you will see ${\displaystyle \pm {\sqrt {x}}}$.