Question

question
write \\(\sqrt{-18}\\) in simplest radical form.

Explanation:

Step1: Separate negative from radical

$\sqrt{-18} = \sqrt{-1 \times 18}$

Step2: Rewrite using imaginary unit $i$

$\sqrt{-1 \times 18} = i\sqrt{18}$

Step3: Factor 18 into perfect square

$i\sqrt{18} = i\sqrt{9 \times 2}$

Step4: Simplify the radical

$i\sqrt{9 \times 2} = i \times \sqrt{9} \times \sqrt{2} = 3i\sqrt{2}$

Answer:

$3i\sqrt{2}$