Question

How do you simplify `sqrt(12x^2y^3)- sqrt(27x^4y)`?

Answer 1

Extract as much as possible from within each of the radicals

`color(red)(sqrt(12x^2y^3))- color(blue)(sqrt(27x^4y))`

`= color(red)(2xysqrt(3y)) - color(blue)(3x^2sqrt(3y))`

`= sqrt(3y)(2xy-3x^2)`

`=sqrt(3y)x(2y-3x)`