Monomial ideals with tiny squares

Let I⊂K[x,y] be a monomial ideal. How small can μ(I2) be in terms of μ(I), where μ denotes the least number of generators? It was widely expected that the inequality μ(I2)>μ(I) should hold whenever μ(I)≥2. Here we disprove this expectation and provide a somewhat surprising answer to the above question.