Period relations for Rankin-Selberg convolutions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$

Using the modular symbol approach, we prove the rationality and period relations for certain critical values of Rankin-Selberg L-functions for $\mathrm{GL}(n)\times\mathrm{GL}(n)$ over any number field that contains a CM field.