SOLUTION: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I deeply appreciate it!! Sums of Radicals Simplify.

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Question 177826This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I deeply appreciate it!!
Sums of Radicals
Simplify. If no simplification is possible, say so.
√2/3(√27/2-3/√2) This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282%2F3%29%28sqrt%2827%2F2%29-3%2Fsqrt%282%29%29%29
...((sqrt(27)/sqrt(2))-(3/sqrt(2)))
...(sqrt(27)-3)/sqrt(2)
...(sqrt(9*3)-3/sqrt(2)
...(3sqrt(3)-3)/sqrt(2)
(sqrt(2)/sqrt(3))(3sqrt(3)-3)/sqrt(2)
=(3sqrt(6)-3sqrt(2))/sqrt(6)
=sqrt(6)((3sqrt(6)-3sqrt(2))/6) Multiply top and bottom by sqrt(6) to eliminate the sqrt(6) in the denominator which is not allowed.
=(3sqrt(36)-3sqrt(12))/6
=(18-3sqrt(4*3))/6
=(18-6sqrt(3))/6
=3-sqrt(3)
.
Ed