Question

Write square root of, minus, 28, end square root
−28
​
in simplest radical form.

Answer 1

The expression \(\sqrt{-28}\) can be simplified using the properties of imaginary numbers.

First, we can rewrite \(-28\) as:

\[
-28 = -1 \times 28
\]

Thus, we can express the square root as:

\[
\sqrt{-28} = \sqrt{-1 \times 28} = \sqrt{-1} \times \sqrt{28}
\]

We know that \(\sqrt{-1} = i\), where \(i\) is the imaginary unit. Now, we simplify \(\sqrt{28}\):

\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}
\]

Putting this back into our expression gives:

\[
\sqrt{-28} = i \times 2\sqrt{7} = 2i\sqrt{7}
\]

Thus, the simplest radical form of \(\sqrt{-28}\) is:

\[
\boxed{2i\sqrt{7}}
\]