What is the simplest form of #sqrt(75x^5)/(sqrt(12xy^2))#?

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Answer 1 · 2018-01-08T21:51:40

#(5x^2)/(2y)#

#sqrt(75x^5)/(sqrt(12xy^2))#

#sqrt(75)/(sqrt(12)# can be simplified:

#sqrt75 = sqrt25 * sqrt3 = 5sqrt3#

#sqrt12 = sqrt4 * sqrt3 = 2sqrt3#

#sqrt(75)/(sqrt(12)) = (5cancel(sqrt(3)))/(2cancel(sqrt(3)))#

#sqrt(x^5)/(sqrt(xy^2))# can be simplified:

#sqrt(x^5)/(sqrt(xy^2)) = ((sqrtx)(sqrtx)^4)/((sqrtx)(sqrty)^2#

#(cancel((sqrtx))(sqrtx)^4)/(cancel((sqrtx))(sqrty)^2#

#= ((sqrtx)^4)/((sqrty)^2#

#= (x^2)/y#

#sqrt(75x^5)/(sqrt(12xy^2)) = (5/2) * x^2/y#

#=(5x^2)/(2y)#