The present paper delineates the conditions that the projective change between two $(\alpha, \beta)$-metrics analyzable. The $ F = \sqrt{\alpha (\alpha + \beta)}$ is considered as a Square root $(\alpha, \beta)$-metric and $\tilde{F} = \frac{\tilde{\alpha^{2}}}{\tilde{\beta}}$ is considered as a Kropina metric on a manifold of dimension $n \geq 2$, where $\alpha$ and $\tilde{\alpha}$ are Riemannian metrics while $\beta$ and $\tilde{\beta}$ are two non-zero 1-forms. The primary objective of this study is to identify the necessary and sufficient conditions for a projective change between Square root $(\alpha, \beta)$-metric and Kropina metric. Furthermore we will discuss some curvature properties on a manifold.