Finding the Alternate Form of a Square Root: A Mathematical Challenge

[Rat3dR]

Hey there,

Square roots never have been my strongest point in maths, but I'm not seeing the trick in this example:

I'm trying to find an alternate form of:
sqrt(3+sqrt(8))
I get as far as:
sqrt(3+2 sqrt(2))

But i know i want to/should end up with:
1+sqrt(2)

I just don't know how to get there... :(

Any help?

Thanks

 

[micromass]

Try squaring both expressions. Then they become equal, no?

 

[Rat3dR]

Maybe i should explain my question a little further..

In my calculations I end up with the first (or second) expression (namely sqrt(3+sqrt(8))).. Which is fine, since it's the right answer, however, for convenience I tried to find an alternate, simpler expression, which should be 1+sqrt(2). I found it using Mathematica, but I have NO idea how I'd go from the first expression to the last one.. What are the intermediate steps?

EDIT: I played around a bit, using your useful input, and i think I'm getting the hang of it.. Any advice on how to tackle these kind of simplifications in general would still be great though :)

 

[yuiop]

I'm trying to find an alternate form of:
sqrt(3+sqrt(8))
I get as far as:
sqrt(3+2 sqrt(2))

But i know i want to/should end up with:
1+sqrt(2)

Try sqrt(3+sqrt(8)) --> sqrt(3+2 sqrt(2)) --> sqrt(1+2+2 sqrt(2)) --> (factorise)--> sqrt( (1+sqrt(2))(1+sqrt(2)) ) --> 1+sqrt(2)

 

[Rat3dR]

Yes, thank you all for your help :). I just needed this little bump to get things going. :)