When you are multiplying roots, you merely multiply what is under the root sign. sqrt(2)*sqrt(3) = sqrt(6). Additionally, sqrt(6) can be simplified to 2*sqrt(3). Can you take it from there?
The problem is just to find the distance between ( ) and ( )
while the book shows;
I simplified the problems on a ti-30 and got the same decimal number for each answer.
So I think I'm just looking for a way to convert between the two forms.
It's not the commutative property that you're using here.
The commutative property has to do with the order in addition and multiplication.
Addition: a + b = b + a
Multiplication: ab = ba
You simply extracted the square root of the largest perfect square factor of 12 and multiplied it by the factor -2 to arrive at your -4 at the end there.
This probably seems silly but, presumably I was taught how too do this specific operation before. And then promptly forgot that it exists. So I'd just like to over learn as much about it as I can so that I remember it for later. So knowing anything extraneous would be helpful.
So far all I can think of is something like; implies ; as some thing additional to hold onto.