Question

Simplify \[\sqrt{3 + 2\sqrt{2}}\].

Answer 1

We are asked to simplify`sqrt(3 +2sqrt2)`.  It can be written in the form   `(a+b)^2 = a^2 +b^2 +2ab` as

`sqrt(3 +2sqrt2) = sqrt(2+1+2xx 1xx sqrt2)`

                      ` = sqrt((sqrt2)^2 + (1)^2 + 2 xx 1 xx sqrt2)`

                      ` = sqrt((sqrt2+1))^2`

                      ` = sqrt2 +1`

Hence the value of given expression is `  sqrt2 +1`.