f(x,y) = (xy)/sqrt(x^2+y^2) Determine whether the function is homogenous and if it is, determine its degree

Given,
f(x,y) = (xy)/sqrt(x^2+y^2)
to check whether it is homogenous or not
f(tx,ty)= (tx ty)/sqrt((tx)^2+(ty)^2)
=(t^2 xy)/(sqrt(t^2(x^2+y^2)))
=(t^2 xy)/(t* sqrt((x^2+y^2)))
=(t xy)/( sqrt((x^2+y^2)))
so this is  of the form
f(tx,ty)=t^n f(x,y)
and so the function f(x,y) is homogenous
and the degree n = 1