If a Queen is a Rook + Bishop, why isn't it worth 8 points?

Because the Q can only one color diagonal at a time.

its only one piece and easier to take care of

It is called synergy. A bishop is relegated to only one color squares where a queen can change its bishop colors.

   It's not "to each his own". It is basic, fundamental good practice to know where you are materially. And when you say "...I don't want to be down a pawn or a minor piece"...what do you think you are doing but counting material?

Edit: Oh, I see, you are a bullet player. Forget anything I said. Speed is all that matters. Do crazy stuff, just do it fast.

As a noob, the rules of thumb for me are : minor pieces = 3, rook 5, queen 9, pawn 1. So I'm willing to trade rook + minor in exchange for queen, but not two rooks. I also follow the rule that knight > bishop in closed positions, and bishop > knight in open ones. These guidelines are gross oversimplifications, but at my level of play they are fairly useful. I can't think quickly so it helps a lot to have simple rules to follow.

   On a point count, it doesn't make sense (as you said) to trade two Rs for a Q. However, there are certain positional or tactical situations where is does make sense.

    For example, who doesn't like to play a game or tactical puzzle where sacrificing the Q is the best possible move?

   Or, if for example, you are up two or three points in an endgame and you get to take out a Q for your two Rs. That might be a good choice too.

   Material strength is very important...but not always the most important.

Harvey makes a good point. One worth paying close attention to.

I won a game recently where I was down a Knight, but my opponent Q-side Rook was undeveloped and blocked in. I was glad to trade active pieces down to simplify and get a mate in. Him having a bad Rook was like having no Rook at all.

Possibly it is because multiple pieces can get in the way of each other. If a Bishop and a Rook could stand on the same square, they would have, for while that state of affairs lasted, the value of a Queen.

My answer is intended for people with good physics knowledge.

A neutron is the sum of a proton and an electron. But to combine them together to make up a neutron, you need some "binding energy". So:

proton + electron + binding energy = neutron

It's the same with queen.

A queen is the sum of a rook and a bishop. But to combine them together to make up a queen, you need some extra energy. This energy is worth one pawn ...

Some systems actually used to give the bishop 4 points. Could have derived from that.

I still think it has to do with the fact that Q can assume the roles of either DSB+R or LSB+R, but not both LSB and DSB. But it can alternate between LSB and DSB.

Physics analogy was pretty good, btw.

I noticed people asking about numerical values.

The only purpose for numerical values is to give a sheer beginner a basis to understand the strength of each piece.

When you get to the higher levels, throw that concept out the Window.  I had an Over the Board game last night where on move 30, I could have taken a Rook with my Knight, and won the Exchange, but the Knight was so dominant that it wasn't worth giving it up for a Rook.  I had a significantly stronger move, played said stronger move, and White resigned 10 moves later.

Depending on the position of each piece in a given game, a Knight could be light years stronger than a Rook in any given position.

+1

All depends on the position.

I think that Wikipedia offers quite a comprehenisve discussion of the whole background for this issue:

https://en.wikipedia.org/wiki/Chess_piece_relative_value

I had always seen that on chess instructions as a kid.  I think the Queen's value was dropped to 9, because most authorities don't believe it's worth sacrificing two rooks for a Queen.  

I hope you get laid soon and calm down. Other than that, I count material yes, but not in numbers. I don't care if someone says the queen is worth (?) 12,5 points, what's the help? BOO.

Where does it say that what you play on chess.com is what you play in real life? Smartass.

Light Bishop=3

Dark bishop=3

Rook=5

3+3+5=11

so then illuminati confirmed

GRANDPA: What type of chess are you talking about?  In blitz chess, I'd agree it is better to have the queen vs rook + bishop, because it is much easier to keep track of the queen.  Change to a two hour game so that there is more time to work out those tricky two-piece maneuvers, and the rook + bishop can put up a much tougher fight.  

Hmm, that gets me wondering.... (Research in progress....) Yep, all you play here is blitz and bullet.  Of course you would think the queen is far superior.       

Hi, I think I have reached objective relative values, but this serves more for chess computing, chess variations with different armies, and exchanges of pieces at grand master level.