Question

Simplify each number using i.
I've had this explained so many times and I just don't get it..

Answer 1

sqrt -7
sqrt -15
sqrt -32
sqrt -72

Answer 2

It turns out that \[\Large i = \sqrt{-1}\]

so what we do is factor each radicand (the stuff under the root) and break up the root like so

\[\Large \sqrt{-7} = \sqrt{-1*7}\]

\[\Large \sqrt{-7} = \sqrt{-1}*\sqrt{7}\]

\[\Large \sqrt{-7} = i\sqrt{7}\]

Answer 3

The second one is done the exact same way

\[\Large \sqrt{-15} = \sqrt{-1*15}\]


\[\Large \sqrt{-15} = \sqrt{-1}*\sqrt{15}\]


\[\Large \sqrt{-15} = i\sqrt{15}\]

Answer 4

The third one is a bit different. You need to factor out the -1 like before, but you also have to factor out 16 since this is the largest perfect square factor.

\[\Large \sqrt{-32} = \sqrt{-1*16*2}\]


\[\Large \sqrt{-32} = \sqrt{-1}*\sqrt{16}*\sqrt{2}\]


\[\Large \sqrt{-32} = i*4*\sqrt{2}\]


\[\Large \sqrt{-32} = 4i\sqrt{2}\]

Answer 5

I'll let you do the last one. Tell me what you get.

Answer 6

thanks i'll do it right now

Answer 7

6i2−−√

Answer 8

6isqrt2

Answer 9

Very good, \[\Large \sqrt{-72} = 6i\sqrt{2}\] is correct

Answer 10

thanks!

Answer 11

you're welcome