Answer :
Given equation is
[tex]x^2+y^2+8x-2y+15=0[/tex]Convert this equation into standard form of circle equation.
[tex]\begin{gathered} x^2+2(4)x+4^2+y^2_{}+2(-1)y+1+15-16-1=0 \\ (x+4)^2+(y-1)^2-2=0 \end{gathered}[/tex]On simplifying,
[tex]\begin{gathered} (x+4)^2+(y-1)^2=2 \\ (x+4)^2+(y-1)^2=(\sqrt[]{2})^2 \end{gathered}[/tex]Hence the radius of the circle is
[tex]\sqrt[]{2}[/tex]