Recently, there has been a surge of interest in square-root higher-order topological insulators (HOTIs) due to their unique topological properties inherited from their squared Hamiltonian. Different from conventional HOTIs, square-root HOTIs support paired corner states that exist in different bandgaps. In this work, we experimentally establish a series of two-dimensional photonic decorated Su-Schrieffer-Heeger (SSH) lattices by using the femtosecond-laser writing technique and thereby directly observe paired topological corner states. Interestingly, the higher-order topological properties of such square-root HOTIs are inherited from the parent Hamiltonian, which contains the celebrated 2D SSH lattice. The dynamic evolution of square-root corner states indicates that they exist in different bandgaps. This work not only provides a new platform to study higher-order topology in optics, it also brings about new possibilities for future studies of other novel HOTIs.