# Alternate form of square root

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

Staff Emeritus
Homework Helper
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 :)

Last edited:
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. :)
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