Question

question
write \\(\sqrt{-150}\\) in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Factor out -1 from radicand

$\sqrt{-150} = \sqrt{-1 \times 150}$

Step2: Split into product of square roots

$\sqrt{-1 \times 150} = \sqrt{-1} \times \sqrt{150}$

Step3: Simplify $\sqrt{-1}$ and factor 150

$\sqrt{-1}=i$, $\sqrt{150}=\sqrt{25 \times 6}$

Step4: Simplify $\sqrt{25 \times 6}$

$\sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}$

Step5: Combine terms

$i \times 5\sqrt{6} = 5i\sqrt{6}$

Answer:

$5i\sqrt{6}$