# Solving √(6 + 3√2) = √a + √b

1. Nov 11, 2013

### BMW

1. The problem statement, all variables and given/known data
Solve the equation √(6 + 3√2) = √a + √b, writing a and b in the form a + b√c.

2. Relevant equations
In the answers they say that a + b = 6, but I cannot see how they can say this.

3. The attempt at a solution
I square both sides, and that is as far as I get:
6 + 3√2 = a + 2√(ab) + b

In the answers, they say from here that a + b = 6. I am clueless as to how they can say this.

Last edited: Nov 11, 2013
2. Nov 11, 2013

### Dick

I don't think they are deducing that from the equation. They are just saying 'let's look for a solution where a+b=6 and 3√2=2√(ab)'. If you can find simple numbers a and b that satisfy that then you've got a simpler form for the radical expression.

Last edited: Nov 11, 2013
3. Nov 11, 2013

### BMW

Ah, ok. So there would be many other solutions, and they are only finding one such solution?

4. Nov 11, 2013

### Dick

Right. There are many other solutions. They are just looking for a nice simple one.

5. Nov 11, 2013

### BMW

So you would also be able to say that a + 2√(ab) = 6 and b = 3√2, and solve that way (with the risk of it being horribly complicated)?

6. Nov 11, 2013

### Dick

Yes, there are lots of ugly solutions.

Last edited: Nov 11, 2013