SOLUTION: My book doesn't explain how to solve: (3√-5)(-4√-12) I'd like to know what to do with the radicands and understand this. So far I thought it was: (3√-1√5

Algebra ->  Rational-functions -> SOLUTION: My book doesn't explain how to solve: (3√-5)(-4√-12) I'd like to know what to do with the radicands and understand this. So far I thought it was: (3√-1√5      Log On


   

Question 895717: My book doesn't explain how to solve:
(3√-5)(-4√-12)
I'd like to know what to do with the radicands and understand this.
So far I thought it was: (3√-1√5)(-4√-1√12) to (3√5)(-4 •2√3) but it doesn't seem right at all and I got stuck. Please help, much thanks!!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Those given factors contain imaginary numbers.
You would be using the idea, i%5E2=-1.

Here is the arithmetic.

3sqrt%28-5%29%28-4%29sqrt%28-12%29
-12%2Asqrt%28-5%29sqrt%28-12%29
-12%2Asqrt%28-1%29sqrt%285%29sqrt%28-1%29sqrt%284%29sqrt%283%29
-12%2Asqrt%28-1%29sqrt%28-1%29sqrt%285%292%2Asqrt%283%29
-12%2A%28-1%29%2A2%2Asqrt%285%29sqrt%283%29
24%2Asqrt%285%29sqrt%283%29
highlight%2824%2Asqrt%2815%29%29


Notice that although the original product shows imaginary numbers, the final result in this example is REAL.

The commutative property for multiplication was used freely where convenient.