A numerical algorithm to extract the square root in radicals from a MV in real Clifford algebras $Cl_{p,q}$ for $n=p+q\le 3$ is presented. We show that in the algebras $Cl_{3,0}$, $Cl_{1,2}$ and $Cl_{0,3}$ there are up to four isolated roots in a case of the most general (generic) MV. The algebra $Cl_{2,1}$ makes up an exception and the MV here can have up to 16 isolated roots. In addition to isolated roots, a continuum of roots can appear in all algebras except $p+q=1$. A number of characteristic examples are provided to illustrate properties of various roots that may appear in $n=3$ Clifford algebras, including the case when there are no roots at all. Also we provide the explicit formulas of roots for some fixed elements of MV (scalar, vectors, bivectors, pseudoscalar and some of their combinations) in a basis-free form which may be useful in applications as well.