If 1/(3 − 2√2) = a + b√2 where a and b are rational numbers, then a + b equals:

Multiply above and below by the conjugate 3 + 2√2. The denominator becomes $3^2-(2\surd 2{)}^2=9-8=1$, so the value is just 3 + 2√2. Hence $a=3,b=2$ and $a+b=5$. Using the conjugate 3 − 2√2 by mistake gives a negative $b$ and the wrong sum 1.