Question
Write square root of, minus, 7, end square root
−7
in simplest radical form.
−7
in simplest radical form.
Answers
GPT-4o mini
The expression \(\sqrt{-7}\) involves taking the square root of a negative number. To express this in simplest radical form, you can use the imaginary unit \(i\), where \(i = \sqrt{-1}\).
Thus, you can rewrite \(\sqrt{-7}\) as:
\[
\sqrt{-7} = \sqrt{7} \cdot \sqrt{-1} = \sqrt{7} \cdot i
\]
So, the simplest radical form of \(\sqrt{-7}\) is:
\[
\sqrt{-7} = i\sqrt{7}
\]
Thus, you can rewrite \(\sqrt{-7}\) as:
\[
\sqrt{-7} = \sqrt{7} \cdot \sqrt{-1} = \sqrt{7} \cdot i
\]
So, the simplest radical form of \(\sqrt{-7}\) is:
\[
\sqrt{-7} = i\sqrt{7}
\]