Question

question
write \\(\sqrt{-7}\\) in simplest radical form.
answer attempt 1 out of 4

Explanation:

Step1: Recall the imaginary unit definition

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \), so we can rewrite \( \sqrt{-7} \) by factoring out \( \sqrt{-1} \).
\( \sqrt{-7} = \sqrt{(-1) \times 7} \)

Step2: Use the property of square roots

Using the property \( \sqrt{ab}=\sqrt{a}\cdot\sqrt{b} \) (for \( a = - 1,b = 7 \) where we consider the imaginary unit for the negative part), we get:
\( \sqrt{(-1)\times7}=\sqrt{-1}\cdot\sqrt{7} \)
Since \( \sqrt{-1}=i \), we substitute that in:
\( \sqrt{-1}\cdot\sqrt{7}=i\sqrt{7} \)

Answer:

\( i\sqrt{7} \)