Question

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

Explanation:

Step1: Separate negative from radical

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

Step2: Simplify $\sqrt{-1}$ to $i$

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

Step3: Factor 150 into perfect square

$\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6}$

Step4: Simplify $\sqrt{25}$ to 5

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

Step5: Combine with imaginary unit

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

Answer:

$5i\sqrt{6}$