Question

simplifying radicals with negative radicands
score: 0/5 penalty: 0.25 off
question
write $sqrt{-27}$ in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Separate negative radicand

$\sqrt{-27} = \sqrt{-1 \times 27}$

Step2: Split into two radicals

$\sqrt{-1 \times 27} = \sqrt{-1} \times \sqrt{27}$

Step3: Simplify $\sqrt{-1}$ and $\sqrt{27}$

$\sqrt{-1} = i$, $\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$

Step4: Combine terms

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

Answer:

$3i\sqrt{3}$