How do you divide #sqrt(12x^3y^12)/sqrt(27xy^2)#?

2 Answers
Mar 22, 2015

Take one big root to get:
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and finally taking the square root:
#=2/3*xy^5#

Hope it helps!

Mar 22, 2015

There are several good approaches to this question:
The reason I try this is that I see some common factors. Namely #3#, #x#, and #y^2#

Write it as a single square root, then simplify, the break it up into smaller square roots.
Or simplify both numerator and denominator, then simplify what you can.

#sqrt(12x^3y^12)/sqrt(27xy^2)=sqrt((12x^3y^12)/(27xy^2))=sqrt((4x^2y^10)/9)=(2xy^5)/3#

Or:

#sqrt(12x^3y^12)/sqrt(27xy^2)=(sqrt(4*3*x^2*x*y^12))/(sqrt(9*3*x*y^2))=(2xy^6sqrt(3x))/(3ysqrt(3x))=(2xy^5)/3#

(Rationalizing the denominator would work too, eventually.)