## Precalculus (6th Edition) Blitzer

The standard form of $\sqrt{-75}-\sqrt{-12}$ is $3i\sqrt{3}$.
Consider the expression, $\sqrt{-75}-\sqrt{-12}$ Rewrite $\sqrt{-75}-\sqrt{-12}$ as $\sqrt{75}\sqrt{-1}-\sqrt{12}\sqrt{-1}$ As $i=\sqrt{-1}$ Therefore, \begin{align} & \sqrt{-75}-\sqrt{-12}=\sqrt{25\left( 3 \right)}i-\sqrt{4\left( 3 \right)}i \\ & =5\sqrt{3}i-2\sqrt{3}i \end{align} Subtract the terms; combine the real part and imaginary part separately. \begin{align} & 5\sqrt{3}i-2\sqrt{3}i=i\sqrt{3}\left( 5-2 \right) \\ & =i\sqrt{3}\left( 3 \right) \\ & =3i\sqrt{3} \end{align} Thus, $\sqrt{-75}-\sqrt{-12}=3i\sqrt{3}$ Hence, the standard form $\sqrt{-75}-\sqrt{-12}$ is $3i\sqrt{3}$.