We have a number, \(x\). The square roots of \(x\) are the numbers which, when squared, equals \(x\). This square root, call it \(y\), is the solution to \[y^2 = x.\]
There’s only one square root of zero (which is zero itself). There are no real square roots for negative numbers. There are two square roots for every other positive number.
We write \(\sqrt{x}\) to represent the positive square root of \(x\). The other root would be \(-\sqrt{x}\).
To write both possible roots, we use the plus or minus sign to get \(\pm\sqrt{x}\).