just use FOIL (First, Outer, Inner, Last).
( √2 - √3 ) X ( √2 - √3 ) First: √2 X √2 = 2 Outer: √2 X -√3 = -√6 Inner: -√3 X √2 = -√6 Last: -√3 X -√3 = 3 and then add them together. 2 - √6 - √6 + 3 5 - 2(√6) The answer is 5 - 2(√6) .