SOLUTION: Homework Help (2 + sqrt3)squared The answer is 7 + 4sqrt3 but I don't know how they got the answer.

Algebra ->  Radicals -> SOLUTION: Homework Help (2 + sqrt3)squared The answer is 7 + 4sqrt3 but I don't know how they got the answer.      Log On


   

Question 145229: Homework Help
(2 + sqrt3)squared
The answer is 7 + 4sqrt3 but I don't know how they got the answer.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Bsqrt%283%29%29%5E2 Start with the given expression


%282%2Bsqrt%283%29%29%282%2Bsqrt%283%29%29 Expand. Remember something like x%5E2=x%2Ax


Now let's FOIL the expression



Remember, when you FOIL an expression, you follow this procedure:


%28highlight%282%29%2Bsqrt%283%29%29%28highlight%282%29%2Bsqrt%283%29%29 Multiply the First terms:%282%29%2A%282%29=4


%28highlight%282%29%2Bsqrt%283%29%29%282%2Bhighlight%28sqrt%283%29%29%29 Multiply the Outer terms:%282%29%2A%28sqrt%283%29%29=2%2Asqrt%283%29


%282%2Bhighlight%28sqrt%283%29%29%29%28highlight%282%29%2Bsqrt%283%29%29 Multiply the Inner terms:%28sqrt%283%29%29%2A%282%29=2%2Asqrt%283%29


%282%2Bhighlight%28sqrt%283%29%29%29%282%2Bhighlight%28sqrt%283%29%29%29 Multiply the Last terms:%28sqrt%283%29%29%2A%28sqrt%283%29%29=%28sqrt%283%29%29%5E2=3


4%2B2%2Asqrt%283%29%2B2%2Asqrt%283%29%2B3 Now collect every term to make a single expression



7%2B4%2Asqrt%283%29 Now combine like terms


---------------------
Answer:
So %282%2Bsqrt%283%29%29%5E2 foils and simplifies to 7%2B4%2Asqrt%283%29

In other words, %282%2Bsqrt%283%29%29%5E2=7%2B4%2Asqrt%283%29