Question

question
write \\(\sqrt{-216}\\) in simplest radical form.

Explanation:

Step1: Factor out -1 from the radicand

$\sqrt{-216} = \sqrt{-1 \times 216}$

Step2: Split the square root

$\sqrt{-1 \times 216} = \sqrt{-1} \times \sqrt{216}$

Step3: Simplify $\sqrt{-1}$ to $i$

$\sqrt{-1} \times \sqrt{216} = i \times \sqrt{216}$

Step4: Factor 216 into perfect square

$\sqrt{216} = \sqrt{36 \times 6}$

Step5: Split and simplify the radical

$\sqrt{36 \times 6} = \sqrt{36} \times \sqrt{6} = 6\sqrt{6}$

Step6: Combine with $i$

$i \times 6\sqrt{6} = 6i\sqrt{6}$

Answer:

$6i\sqrt{6}$