SOLUTION: How do I solve this problem? (Sqrt of 3 + sqrt of 5)(sqrt of 3 + sqrt of 5) This is multiplication...

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Question 719087: How do I solve this problem?
(Sqrt of 3 + sqrt of 5)(sqrt of 3 + sqrt of 5)
This is multiplication...
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%283%29+%2B+sqrt%285%29%29%28sqrt%283%29+%2B+sqrt%285%29%29
Don't let the square roots distract you. This is one two-term expression times another two-term expression. You can use FOIL to multiply them.

But if we look closer, the two two-term expressions are exactly the same. We could rewrite the expression as:
%28sqrt%283%29+%2B+sqrt%285%29%29%5E2
So not only can we use FOIL we can use a factoring pattern:
%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2
to multiply. Using the pattern is faster and easier than FOIL so I will use the pattern. In our expression, our "a" is sqrt%283%29 and our "b" is sqrt%285%29. So according to the pattern
%28sqrt%283%29+%2B+sqrt%285%29%29%5E2
will be equal to
%28sqrt%283%29%29%5E2+%2B+2%2Asqrt%283%29%2Asqrt%285%29%2B+%28sqrt%285%29%29%5E2
Simplifying...
3+%2B+2%2Asqrt%2815%29%2B+5
8+%2B+2%2Asqrt%2815%29
This is the answer. (If you had used FOIL correctly you would have gotten the same thing.)