#sqrt((75xy^7)/(12xy))# #=sqrt((cancel(3)*25*cancel(x)*cancel(y)*y^6)/(cancel(3)*4*cancel(x)*cancel(y))# {cancelling out common terms in numerator and denominator, and using law of indices #x^a*x^b = x^(a+b)#} #=sqrt((5y^3)^2/2^2)# #=(5/2 y^3)^(2*1/2)#{using the fact that square roots are same as power 1/2, cube roots as power 1/3 and nth roots are same as power 1/n} #=5/2 y^3#