Question

√-54 ​ in simplest radical form.

Answer 1

To simplify \( \sqrt{-54} \), we can first express the negative square root in terms of imaginary numbers. Recall that \( \sqrt{-1} \) is denoted as \( i \).

So, we can break down \( \sqrt{-54} \) as follows:

\[
\sqrt{-54} = \sqrt{-1 \cdot 54} = \sqrt{-1} \cdot \sqrt{54} = i \cdot \sqrt{54}
\]

Next, we need to simplify \( \sqrt{54} \). We can factor \( 54 \) into its prime factors:

\[
54 = 2 \times 3^3
\]

Now we can simplify \( \sqrt{54} \):

\[
\sqrt{54} = \sqrt{2 \times 3^3} = \sqrt{2} \cdot \sqrt{3^3} = \sqrt{2} \cdot 3\sqrt{3} = 3\sqrt{6}
\]

Putting it all together, we have:

\[
\sqrt{-54} = i \cdot \sqrt{54} = i \cdot 3\sqrt{6}
\]

Thus, in simplest radical form, the solution is:

\[
\sqrt{-54} = 3i\sqrt{6}
\]