Question

Express the radical using the imaginary unit, i.

Answer 1

The foundation of imaginary numbers is that $i = \sqrt{-1}$.

When simplifying radicals involving square roots of negative numbers, your first step is to separate the negative from the number and turn it into $i$.

    $\begin{aligned}\sqrt{-14} &= \sqrt{-1 \cdot 14}\\[0.5em] &= \sqrt{-1 }\cdot \sqrt{14}\\[0.5em] &= i\cdot \sqrt{14}\end{aligned}$

At this point, you can turn to the $\sqrt{14}$ and decide if this can be simplified or not.  (Ask youself if there are any perfect squares that divide into 14.)