square root of a Riemannian metric

Question

Let $(M,g)$ be a compact Riemannian manifold. Taking a smooth vector field $X$, there is an associated smooth function $$g(X,X):M\longrightarrow \mathbb{R}^+, \quad p\longmapsto g_p(X_p,X_p)\geq 0.$$ I would like to know if there are a finite number of smooth functions $f_i$ $\in$ $C^{\infty}(M)$ such that $$g(X,X)=\sum_i f^2_i.$$