SOLUTION: 4√3+2√7-4√18 how can u simplfy it. I know you simplify each radical then combine but i do not know how to simplify a radical

Algebra.Com
Question 550173: 4√3+2√7-4√18 how can u simplfy it. I know you simplify each radical then combine but i do not know how to simplify a radical
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20086)   (Show Source): You can put this solution on YOUR website!
4√3+2√7-4√18
You can't do much with that, except to simplify the
last term.  Are you sure you didn't copy something
wrong?

 +  - 

We can't break or 3 or 7, but we can break up 18
into primes like this 2×3×3 and since there are two 3's 
there, that's 9, which is a perfect square. And we know
that the square root of 9 is 3. So we copy everything
over and write 9×2 instead of 18:

 +  - 

The square root of a product (multiplication) is the
product (multiplication) of the square roots, so we
can write  as  

 +  - 

and since we know that  is 3, we can write
that last term up there as 

 +  - 4×3×

and since 4×3 is 12 we can have

4 + 2 - 12

But there is nothing else you can do in the way of
simplifying radicals.  

If that 3 had been a 2, or the 7 had been a 2 or a 3
or the 2 a 7, then we could have combined some terms, 
but as it is all we could do was simplify the last term
and leave the first two terms as they were to begin with.

There is one thing we can do, but it it is not necessary,
and that is to take out a 2 factor:

2( +  - )
  
Edwin
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!