Question

√-50
in simplest radical form.
Answer
Attempt 1 out of 2

Answer 1

To simplify the expression \(\sqrt{-50}\), we can use the property of imaginary numbers.

1. First, we can break \(-50\) into its factors:
\[
-50 = -1 \times 50
\]

2. We know that \(\sqrt{-1} = i\), where \(i\) is the imaginary unit. Thus, we can write:
\[
\sqrt{-50} = \sqrt{-1 \times 50} = \sqrt{-1} \times \sqrt{50} = i \sqrt{50}
\]

3. Next, we simplify \(\sqrt{50}\). The number \(50\) can be factored as:
\[
50 = 25 \times 2 = 5^2 \times 2
\]

4. Therefore:
\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
\]

5. Substituting this back into the expression gives:
\[
\sqrt{-50} = i \sqrt{50} = i \times 5\sqrt{2} = 5i\sqrt{2}
\]

Thus, the simplest radical form of \(\sqrt{-50}\) is:
\[
\boxed{5i\sqrt{2}}
\]