Question

simplifying radicals with negative radicands
score: 4/5 penalty: 0.25 off
question
write $sqrt{-75}$ in simplest radical form.
answer attempt 1 out of 2
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Explanation:

Step1: Separate negative radicand

$\sqrt{-75} = \sqrt{-1 \times 75}$

Step2: Split the radical

$\sqrt{-1 \times 75} = \sqrt{-1} \times \sqrt{75}$

Step3: Simplify $\sqrt{-1}$ and $\sqrt{75}$

$\sqrt{-1}=i$, $\sqrt{75}=\sqrt{25 \times 3}=5\sqrt{3}$

Step4: Combine the terms

$i \times 5\sqrt{3} = 5i\sqrt{3}$

Answer:

$5i\sqrt{3}$