The Milnor-Moore theorem states that for path-connected H-spaces $X$, $H\_\*(X;\Bbb Q)$ is a free graded-commutative algebra on $\pi\_\*(X)\otimes \Bbb Q$. I am asked to use this to compute $\pi\_i(S^n)\otimes \Bbb Q$.

I know another way of computing $\pi\_i(S^n)\otimes \Bbb Q$ which does not use the Milnor-Moore theorem. I'm not sure how one would use this theorem since the only spheres which are H-spaces are in dimensions 1,3 and 7.