Simplifying √(3+2√(2)): Find the Integer and Irrational

[chillfactor]

Homework Statement

√(3+2√(2)) can be simplified into a fairly simple sum of two number: one is an integer and one is an irrational number . Find them and show you are correct by squaring both sides of the "equation"

Homework Equations

The Attempt at a Solution

 

[eumyang]

Here's a hint: note that
\sqrt{3 + 2\sqrt{2}} = \sqrt{1 + 2\sqrt{2} + 2}

 

[chillfactor]

isnt that illegal. By the same logic I could simplify the square root of nine to the square root of 9 ones and solve and get nine

 

[The legend]

the whole thing is under the square root .. it won't result to 9.

 

[Office_Shredder]

Isn't what illegal? All he did was say that 3=2+1. he didn't break up the square root

 

[HallsofIvy]

Writing \sqrt{9}= \sqrt{1+ 1+ 1+ 1 +1 + 1+ 1+ 1+ 1} is perfectly legal.

It is thinking that that last is the sum of
\sqrt{1}+ \sqrt{1}+ \sqrt{1}+ \sqrt{1}+ \sqrt{1}+ \sqrt{1}+ \sqrt{1}+ \sqrt{1}+ \sqrt{1}

that is illegal.

 

[HallsofIvy]

Sorry. I have removed the "answer" to the problem.