Question

question
write \\(\sqrt{-2}\\) in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Recall imaginary unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). So we can rewrite \( \sqrt{-2} \) by factoring out \( \sqrt{-1} \).
\( \sqrt{-2} = \sqrt{(-1)\times2} \)

Step2: Use radical property

Using the property of radicals \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\geq0 \); here we extend it to complex numbers with \( a = - 1,b = 2 \)), we get \( \sqrt{(-1)\times2}=\sqrt{-1}\times\sqrt{2} \)
Since \( \sqrt{-1}=i \), then \( \sqrt{-1}\times\sqrt{2}=i\sqrt{2} \)

Answer:

\( i\sqrt{2} \)