Square root

Summary

\[x^2=a\]

\(2\) and \(-2\) are square roots of \(4\) (as \(2^2={\left( -2 \right)}^2=4\) )
For \(a≥0\) , the equation \(x^2=a\) has a unique real non-negative solution
For \(a<0\) , the equation \(x^2=a\) has no real solution
For \(a≥0\) , the unique real non-negative solution to the equation is called the principal square root of \(a\) .
The principal square root of \(a\) is denoted by \(\sqrt{a}\) or \(\sqrt[2]{a}\) or \(a^{1/2}\) or. Thus, \(\sqrt{4}=2\) , not \(±2\) .