Question 895717
Those given factors contain imaginary numbers.
You would be using the idea, {{{i^2=-1}}}.


Here is the arithmetic.


{{{3sqrt(-5)(-4)sqrt(-12)}}}

{{{-12*sqrt(-5)sqrt(-12)}}}

{{{-12*sqrt(-1)sqrt(5)sqrt(-1)sqrt(4)sqrt(3)}}}

{{{-12*sqrt(-1)sqrt(-1)sqrt(5)2*sqrt(3)}}}

{{{-12*(-1)*2*sqrt(5)sqrt(3)}}}

{{{24*sqrt(5)sqrt(3)}}}

{{{highlight(24*sqrt(15))}}}



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.