Question

simplifying radicals with negative radicands
score: 0/7 penalty: 0.5 off
question
write $sqrt{-40}$ in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Factor out -1 from radicand

$\sqrt{-40} = \sqrt{-1 \times 40}$

Step2: Split into product of radicals

$\sqrt{-1 \times 40} = \sqrt{-1} \times \sqrt{40}$

Step3: Simplify $\sqrt{-1}$ and factor 40

$\sqrt{-1}=i$, $\sqrt{40}=\sqrt{4 \times 10}$

Step4: Simplify $\sqrt{4 \times 10}$

$\sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}$

Step5: Combine terms

$i \times 2\sqrt{10} = 2i\sqrt{10}$

Answer:

$2i\sqrt{10}$