Question

Write square root of, minus, 50, end square root
−50
​
in simplest radical form.

Answer 1

To express the square root of \(-50\) in simplest radical form, we start by separating the negative sign from the square root:

\[
\sqrt{-50} = \sqrt{50} \cdot \sqrt{-1}
\]

The square root of \(-1\) is represented by the imaginary unit \(i\):

\[
\sqrt{-1} = i
\]

Next, we simplify \(\sqrt{50}\):

\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}
\]

Putting it all together, we have:

\[
\sqrt{-50} = \sqrt{50} \cdot i = 5\sqrt{2} \cdot i
\]

Thus, the final simplified form of \(\sqrt{-50}\) is:

\[
5\sqrt{2}i
\]