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In this note, we study various measures of irrationality for hypersurfaces inprojective spaces which were recently proposed by Bastianelli, De Poi, Ein,Lazarsfeld and Ullery. In particular, we answer the question raised byBastianelli that if $X \subset P^{n+1}$ is a very general smooth hypersurfaceof dimension $n$ and degree $d\geq 2n+2$, then$\text{stab.irr}(X)=\text{uni.irr}(X)=d-1$. As a corollary, we prove that$\text{irr}(X\times P^{m})=\text{irr}(X)$ for any integer $m\geq 1$.

On irrationality of hypersurfaces In $\mathbf{P}^{n+1}$