SOLUTION: Simplify in simplest radical form Not sure if I have these right or I have to go further {{{3 sqrt(2) + 5 sqrt( 2 )}}} I get {{{(3+5) sqrt( 2 ) = 8 sqrt(2)}}} And {{{3 sqrt(

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify in simplest radical form Not sure if I have these right or I have to go further {{{3 sqrt(2) + 5 sqrt( 2 )}}} I get {{{(3+5) sqrt( 2 ) = 8 sqrt(2)}}} And {{{3 sqrt(      Log On


   

Question 202704This question is from textbook
: Simplify in simplest radical form
Not sure if I have these right or I have to go further
3+sqrt%282%29+%2B+5+sqrt%28+2++%29
I get %283%2B5%29+sqrt%28+2+%29+=+8+sqrt%282%29
And
3+sqrt%288%29+%2B+2+sqrt%2816%29
I get %283%2B2%29+%2B+sqrt%2824%29+=+5+%2B+sqrt%2824+%29
I'd appreciate it if someone could tell me if these are right This question is from textbook

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
3sqrt%282%29+%2B+5sqrt%28+2++%29
I get %283%2B5%29+sqrt%28+2+%29+=+8+sqrt%282%29
This is exactly right. The only reason you are allowed to add 3sqrt%282%29+%2B+5sqrt%28+2++%29 is that the square roots are the same. It is very much like adding 3x and 5x and getting 8x. We add them using the Distributive Property (in reverse). This is also the reason the second problem is incorrect. The square roots are different.
The correct way to simplify
3sqrt%288%29+%2B+2sqrt%2816%29
is to start by simplifying each square root. The sqrt%2816%29 is simply 4. The sqrt%288%29 is not so easy. We start by trying to find perfect square factors in 8. We should find that 8 = 4*2 (with 4 being the perfect square, of course). So sqrt%288%29+=+sqrt%284%2A2%29. Now we can use one of the basic properties of square roots: sqrt%28a%2Ab%29+=+sqrt%28a%29+%2A+sqrt%28b%29 to split our square root into the product of square roots: sqrt%284%2A2%29+=+sqrt%284%29%2Asqrt%282%29. Now that sqrt%284%29 is separate we can replace it with 2 giving sqrt%288%29+=+sqrt%284%2A2%29+=+sqrt%284%29+%2A+sqrt%282%29+=+2%2Asqrt%282%29

Putting this all together we get:
3%2Asqrt%288%29+%2B+2sqrt%2816%29+=+3%2A2%2Asqrt%282%29+%2B+2%2A4+=+6%2Asqrt%282%29+%2B+8
and we can go no further. 6%2Asqrt%282%29 and 8 are unlike terms in much the same way that 6x and 8 are unlike terms. You just cannot add them. So we are finished.