解:?$(1)$?∵?$3a + 1$?的立方根是?$-2,$?∴?$3a + 1=(-2)^3=-8,$?解得?$a=-3$?
∵?$2b - 1$?的算術(shù)平方根是?$3,$?∴?$2b - 1=3^2=9,$?解得?$b=5$?
∵?$\sqrt {36}=6,$??$\sqrt {49}=7,$?∴?$\sqrt {43}$?的整數(shù)部分?$c=6$?
?$ (2) 2a - b+\frac 92c=2×(-3)-5+\frac 92×6=-6 - 5 + 27=16$?
∴?$2a-b+\frac 92c $?的平方根是?$\pm 4$?