when combining the roots:

[brian1981us]

1. (sq root symbol)x^2y^3 + 3x^2y^3
2. (sq root symbol)4x^2 2y^3 ---> why is this wrong, I am lost because you combine the x's to get 4x^2, why is 2y^3 wrong?

[rfernandez]

I'll omit the square root sign, as your question is about the expression inside it

Your question is all about combining like terms. Consider these analogous examples:

x + 3x --> 4x
y + 3y --> 4y
xy + 3xy --> 4xy
(x^2)(y^3) + 3(x^2)(y^3) = 4(x^2)(y^3)

So what's actually happening is that you're adding ONE (x^2)(y^3) and THREE (x^2)(y^3)'s to get FOUR (x^2)(y^3)'s.

Taken another way, you could view this as a factoring problem, wherein you "pull out" the common factor (x^2)(y^3):

(x^2)(y^3) + 3(x^2)(y^3)
(x^2)(y^3) (1 + 3)
(x^2)(y^3) (4)
4(x^2)(y^3)