square vs square up

square is a noun but square up is not a noun.

Word	Noun	Adjective	Verb	Adverb
square	Yes	Yes	Yes	Yes
square up	No	No	Yes	No

As verbs, square and square up are synonyms defined as:

As verbs, square up is a hyponym of square; that is, square up is a word with a more specific, narrower meaning than square:

Other hyponyms of square include even up, jog.

square (noun)	square up (noun)
a hand tool consisting of two straight arms at right angles; used to construct or test right angles
any artifact having a shape similar to a plane geometric figure with four equal sides and four right angles
an open area at the meeting of two or more streets
a formal and conservative person with old-fashioned views
someone who doesn't understand what is going on
the product of two equal terms
(geometry) a plane rectangle with four equal sides and four right angles; a four-sided regular polygon
something approximating the shape of a square

square (adjective)	square up (adjective)
having four equal sides and four right angles or forming a right angle
characterized by honesty and fairness
rigidly conventional or old-fashioned
without evasion or compromise
leaving no balance
providing abundant nourishment

square (verb)	square up (verb)
make square	make square
raise to the second power	settle conclusively; come to terms
turn the oar, while rowing	even up the edges of a stack of paper, in printing
turn the paddle; in canoeing
position so as to be square
pay someone and settle a debt
be compatible with
cause to match, as of ideas or acts