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(a) \(m^2 + \cfrac{1}{m^2}\)
\(=\left(m+\cfrac{1}{m}\right)^2-2.m.\cfrac{1}{m}\)
\(=(\sqrt3)^2-2\)
\(=3-2\)
\(=1\) (Answer)

(b) \(m^3 + \cfrac{1}{m^3}\)
\(=\left(m+\cfrac{1}{m}\right)^3-3.m.\cfrac{1}{m}\left(m+\cfrac{1}{m}\right)\)
\(=\left(\sqrt3\right)^3-3.\cancel{m}.\cfrac{1}{\cancel{m}}\times \sqrt3\)
\(=3\sqrt3-3\sqrt3\)
\(=0\) (Answer)