Explanation:
0.3333333333.... = 1/3
0.2222222222... = 1/3 / 3 × 2 = 2/9
so, we now know all the involved fractions.
(1/3 - 1)² - sqrt(1 - 3/2/2) + 2/9
(-2/3)² - sqrt (1 - 3/4) + 2/9
4/9 - sqrt(1/4) + 2/9
6/9 - 1/2
2/3 - 1/2
to calculate that we need to bring both fractions to the same denominator (6).
2/2 × 2/3 - 3/3 × 1/2 = 4/6 - 3/6 = 1/6
so, the complete result is 1/6.