What can we learn about the density dependence of nuclear symmetry energy E sym (ρ) from precise measurements of the radius (R 1.4 ) and/or tidal polarizability (Λ 1.4 ) of canonical neutron stars (NSs) with a mass of 1.4 M ⊙ ? With the E sym (ρ) parameterized using three parameters L, K sym , and J sym which have the asymptotic meaning of being respectively the slope, curvature, and skewness of symmetry energy at saturation density, we found that, while both the R 1.4 and Λ 1.4 depend strongly on the slope L, the K sym and J sym parameters characterizing the high-density behavior of E sym (ρ) also play appreciable roles. Thus, there is not a simple relation between the Λ 1.4 /R 1.4 and L alone. Precise measurements of just the Λ 1.4 and R 1.4 can not completely determine the E sym (ρ) but limit combinations of its parameters. In particular, stringent constraints approximately independent of the J sym on the L-K sym correlations can be obtained. However, infinite combinations of the larger (smaller) L and smaller (larger) K sym can lead to the same Λ 1.4 and R 1.4 . Additional observables including those from terrestrial nuclear experiments are thus necessary to break this degeneracy in order to completely determine the density dependence of nuclear symmetry energy E sym (ρ).