Friendly Surds

The Problem:

Square roots of most numbers are irrational � infinitely long strings of non-recurring decimal digits, with no discernible pattern to them.

Sometimes, however, you find rather strange things happening�

Try adding together.

Then square this new number.

What have you accidentally found the value of?

So, , for some integer value N.

Now try finding what

give you the value of.

Can you make up your own combination of �friendly� surds that behave like this?

You can use more than two surds, or subtraction instead of addition�