Aus Online Mathematik Brückenkurs 1

The number \displaystyle 4 can be written as \displaystyle 4=2\centerdot 2=2^{2} and then, using the power rules, we obtain

\displaystyle 4^{\frac{1}{2}}=\left( 2^{2} \right)^{\frac{1}{2}}=2^{2\centerdot \frac{1}{2}}=2^{1}=2

NOTE: another way to denote \displaystyle 4^{\frac{1}{2}} is \displaystyle \sqrt{4} (the root of \displaystyle 4 ); more on this in the section on roots later in the course.