'squarishness' originates from English, specifically the word 'squarish' combined with the suffix '-ness', where the suffix '-ish' meant 'having the quality of' and '-ness' formed nouns denoting a state or condition.

'squarish' changed from the adjective 'square' (from Middle English 'squar(e)') plus the suffix '-ish'; 'square' itself ultimately derives from Old French (e.g. 'esquare'/'esquarre') and Latin 'quadratus', leading to the modern English 'square' and derivatives like 'squarish' and then 'squarishness'.

Initially, it meant 'having qualities of a square' (i.e., somewhat square); over time the derivative noun 'squarishness' came to denote the state or degree of being somewhat square.