This is confusing me. The book's method is basically this...
Problem:
4

(Radical) 7
Multiply by
(Radical) 7

(Radical) 7
with (Radical) meaning the checkmark thing, and the hyphens being a division line.
That multiplication gets you...
4 * (Radical) 7

7
Which the book marks as correct.
That's all well and good, but I'm confused by the next step up...
What would I do on a problem like this?
2 * (Radical) 3

(Radical) 6
I tried that method, and couldn't do it. The book gives no other methods.
Help please...?
Here is one way of doing this:
since we see that our expression becomes
There is a theorem that says given that both
So, we then see that our expression becomes
Here is another:
Using this idea when we can maninpulate the demonimator a little bit:
Now, the term cancels out.
So we are left with
Now rationalize this expression to get
I hope this makes sense!
Chris
EDIT: Moo beat me!
Alright, I get it now. Thanks!
Edit: Found more that I can't figure out. It's not my day today...>_>
How would I solve problems like these:
(Radical) 5

(Radical) 10
(Radical) 27

(Radical) 45
(Radical) 32

(Radical) 5
Or
(Radical) 18

3 * (Radical) 2