Sqrt(3/2)
√(3/2), the neutral third, is a radical interval of about 351 cents, in the √2.√3 subgroup. It appears in hemipyth as one of the generators, alongside √2/1. It is the unique interval with the property that when stacked twice, it leads to a perfect fifth 3/2, and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.
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In temperaments
Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. 24edo, 41edo) have an approximation to √(3/2).