Question

question
write \\(\sqrt{-10}\\) in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Recall the imaginary unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). So we can rewrite \( \sqrt{-10} \) as \( \sqrt{10 \times (-1)} \).

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 have \( \sqrt{10\times(-1)}=\sqrt{10}\times\sqrt{-1} \).

Step3: Substitute the imaginary unit

Since \( \sqrt{-1} = i \), we get \( \sqrt{10}\times i = i\sqrt{10} \).

Answer:

\( i\sqrt{10} \)