Question

Please explain how to do the following, involves the imaginary number i:
√-75 - √-12

Answer 1

I'll show you how to simplify √-75

Answer 2

\[\Large \sqrt{-75} = \sqrt{-1*25*3}\]

\[\Large \sqrt{-75} = \sqrt{-1}*\sqrt{25}*\sqrt{3}\]

\[\Large \sqrt{-75} = i*5*\sqrt{3}\]

\[\Large \sqrt{-75} = 5i*\sqrt{3}\]

Notice how on the first line I factored -75 into -1*25*3. I did so to pull out the -1 and to factor 75 as a product of two numbers. One of the numbers is a perfect square.