Positive square root in a C-star algebra ($a^{1/2}$)

Every positive element of a C-star algebra $a$ has a unique positive element $a^{1/2}$ satisfying $(a^{1/2}{)}^2=a$. It is obtained by applying the continuous functional calculus to $t\mapsto \sqrt{t}$ on $\sigma (a)\subseteq [0,\infty )$.