# Algebra/Square Root is Positive

## 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 ${\displaystyle \pm {\sqrt {x}}}$ .