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 - 2 xx 1 xx sqrt2)`

                        ` = sqrt((sqrt2)^2 + (1)^2 - 2xx 1xxsqrt2)`

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

                         `  = sqrt2 - 1`

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