How do you simplify # sqrt ((75xy^7)/(12xy))#?

1 Answer
Jul 23, 2016

Answer:

#5/2 y^3#

Explanation:

#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#