Question

question
write $sqrt{-75}$ in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Separate negative from radical

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

Step2: Split into product of radicals

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

Step3: Simplify $\sqrt{75}$

$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$

Step4: Substitute $\sqrt{-1}=i$

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

Answer:

$5i\sqrt{3}$