combining

[latresa31s]

When I am to combine am I suppose to combine the like terms in this problem.


2y√ [27x^3z] - 3x√ [3xy^2z]


Thanks in advance for the help.

 

[stapel]

You can't combine until you have "like" terms, and you don't yet.

In this case, though, there might not be any combining; first, you need to simplify the radicals. There may be more you can do after that -- or not. But you won't know until you take care of the radicals.

Are the radicals square roots?

Eliz.

 

[Denis]

When I am to combine am I suppose to combine the like terms in this problem.
2y√ [27x^3z] - 3x√ [3xy^2z]
Thanks in advance for the help.

Start with the radicals; rearrange such that you have a term you can take the square root of:

sqrt(27 x^3 z) = sqrt(9x^2 * 3xz) = 3x sqrt(3xz)

sqrt(3 x y^2 z) = sqrt(y^2 * 3xz) = y sqrt(3xz) : ahhh...lucky: sqrt(3xz) in both cases!

Now rewrite expression:
2y(3x)sqrt(3xz) - 3x(y)sqrt(3xz)
= 6xy sqrt(3xz) - 3xy sqrt(3xz)
= 3xy sqrt(3xz) : Bingo!

If you have a hard time following what I did with the radicals:
take sqrt(20)
that's sqrt(4 * 5), right?
and sqrt(4) = 2, right?
so sqrt(20) = 2 sqrt(5)

So the "plan of attack" is to break down the radical into a multiplication
that contains a square, like the "4" in above example; sometimes, this
will not work, like with sqrt(13) : capish?