Want to show: If $X$ is a positive-definite bilinear form on a vector space $G$ with real-valued scalars and $v\in G$, then $\left(X(v,v)\right)^{\frac{1}{2}}$ defines a norm on $G$.
Thus far I have three of the four properties of a norm. What remains to be shown is that $\left(X(u+v,u+v)\right)^{\frac{1}{2}} \leq \left(X(u,u)\right)^{\frac{1}{2}} + \left(X(v,v)\right)^{\frac{1}{2}}$. I need a hint on this remaining property.