Aus Online Mathematik Brückenkurs 1

Looking first at \displaystyle \sqrt{18} this square root expression can be simplified by writing \displaystyle \text{18} as a product of its smallest possible integer factors

\displaystyle 18=2\centerdot 9=2\centerdot 3\centerdot 3=2\centerdot 3^{2}

and then we can take the quadratic out of the square root sign by using the rule \displaystyle \sqrt{a^{2}b}=a\sqrt{b},

\displaystyle \sqrt{18}=\sqrt{2\centerdot 3^{2}}=3\sqrt{2}

In the same way, we write \displaystyle 8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3} and get

\displaystyle \sqrt{8}=\sqrt{2\centerdot 2^{2}}=2\sqrt{2}

All together, we get

\displaystyle \begin{align} & \sqrt{18}\sqrt{8}=3\sqrt{2}\centerdot 2\sqrt{2}=3\centerdot 2\centerdot \left( \sqrt{2} \right)^{2} \\ & =3\centerdot 2\centerdot 2=12 \\ & \\ \end{align}