Using a data sample of $448times10^{6}$ $psi(3686)$ events collected with the BESIII detector operating at the BEPCII storage ring, the decays $psi(3686)rightarrowgammaeta$ and $psi(3686)rightarrowgammapi^{0}$ are observed with a statistical significance of $7.3sigma$ and $ 6.7sigma$, respectively. The branching fractions are measured to be $mathcal{B}(psi(3686)rightarrowgammaeta)=(0.85pm0.18pm0.05)times10^{-6}$ and $mathcal{B}(psi(3686)rightarrowgammapi^{0})=(0.95pm0.16pm0.05)times10^{-6}$. In addition, we measure the branching fraction of $psi(3686)rightarrowgammaeta$ to be $mathcal{B}(psi(3686)rightarrowgammaeta)=(125.1pm2.2pm6.2)times 10^{-6}$, with improved precision compared to previous results.
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