Question

question
write \\(\sqrt{-24}\\) in simplest radical form.

Explanation:

Step1: Recall the imaginary unit

We know that \( \sqrt{-1} = i \), so we can rewrite \( \sqrt{-24} \) as \( \sqrt{24 \times (-1)} \).

Step2: Use the property of square roots

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\geq0 \), but here we extend it for the imaginary case), we get \( \sqrt{24}\times\sqrt{-1} \).

Step3: Simplify \( \sqrt{24} \)

Factor 24: \( 24 = 4\times6 \), so \( \sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6} \).

Step4: Substitute back

Since \( \sqrt{-1}=i \), we have \( 2\sqrt{6}\times i = 2i\sqrt{6} \).

Answer:

\( 2i\sqrt{6} \)