Question

look at the example below which shows how the product property of radicals is used to simplify a radical.
$sqrt{-36} = sqrt{36}sqrt{-1} = 6i$
use the product property of radicals to simplify the following radical.
$sqrt{-81} = 9i$
complete
simplify $sqrt{-50}$.
○ $5sqrt{2}$
○ $5isqrt{2}$
○ $-5sqrt{2}$
○ $-5isqrt{2}$
done

Explanation:

Step1: Split radical into real/imaginary parts

$\sqrt{-50} = \sqrt{50 \times -1} = \sqrt{50} \times \sqrt{-1}$

Step2: Simplify real radical factor

$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$

Step3: Substitute imaginary unit

$\sqrt{-1} = i$, so combine terms: $5\sqrt{2} \times i = 5i\sqrt{2}$

Answer:

B. $5i\sqrt{2}$