Question

Simplify.
5 times the square root of - 24 * 3 times the square root of -18

Answer 1

Oh wait

Answer 2

It's 5 times the square root of -24 X 3 times the square root of -18

Answer 3

Yea I read that wrong. Our equation is 3*(sqrt-18) first. Sorry

Answer 4

Our first problem is 5 times the square root of -24

Answer 5

No actually if the problem is: 5 times the square root of - 24 * 3 times the square root of -18. It is 5*(sqrt-24)(3*sqrt18)

Answer 6

Since this is our equation I chose to start with 3*sqrt of 18

Answer 7

Do you understand?

Answer 8

\[5\sqrt{-24} * 3\sqrt{-18}\]

Answer 9

Okay. Well in either case need to know how to square negatives. To do this we need to use the imaginary unit i. The equation for that will be
i=(-1)^(1/2).
Now we substitute i with our negative:
-24=-24*-1
Understand so far?

Answer 10

Okay, what I have so far is \[5\sqrt{4} * \sqrt{6} * \sqrt{-1} = 5\sqrt{-24} (and) 3\sqrt{9} * \sqrt{2} * \sqrt{-1} = 3 \sqrt{-18}\]

Answer 11

I know the answer is -180 times the square root of 3. I just need to know how to work it out

Answer 12

Hm.. Well I used the imaginary unit and simplified 5sqrt-24 to 10i sqrt6.
Then for 3sqrt -18 I got 9i sqrt2. Then I multiplied to get -180 sqrt 3.
So it'd be 5*sqrt 24 simplified by 3*sqrt18 simplified. (Sorry for the wait)

Answer 13

\[5\sqrt{-24} * 3\sqrt{-18}\]\[5i\sqrt{4*6} * 3i\sqrt{6*3}\]\[15i^2\sqrt{4}\sqrt{6}\sqrt{6}\sqrt{3}\]\[-15*2*6\sqrt{3}\]\[-180\sqrt3\]

Answer 14

what if I\[\sqrt{9} \sqrt{2}\] used

Answer 15

@ChmE

Answer 16

Then the sqrt of 6 wouldn't be able to multiply together

Answer 17

what would I get then

Answer 18

\[15i^2\sqrt{4}\sqrt{6}\sqrt{9}\sqrt{2}\]\[15i^2*2*3\sqrt{6}\sqrt{2}\]\[90i^2\sqrt{12}\]\[90i^2\sqrt{4}\sqrt3\]\[-180\sqrt3\]Looks like the same answer just more work

Answer 19

it's okay as long as it's the same answer