SOLUTION: I really need help solving the following problem. Any assistance you can provide me with will be greatly appreciated. Thanks! (square root of 3 + square root of 2)^2

Algebra ->  Radicals -> SOLUTION: I really need help solving the following problem. Any assistance you can provide me with will be greatly appreciated. Thanks! (square root of 3 + square root of 2)^2      Log On


   

Question 169974: I really need help solving the following problem. Any assistance you can provide me with will be greatly appreciated. Thanks!
(square root of 3 + square root of 2)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28sqrt%283%29%2Bsqrt%282%29%29%5E2 Start with the given expression.


%28sqrt%283%29%2Bsqrt%282%29%29%28sqrt%283%29%2Bsqrt%282%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%28sqrt%283%29%29%2Bsqrt%282%29%29%28highlight%28sqrt%283%29%29%2Bsqrt%282%29%29 Multiply the First terms:%28sqrt%283%29%29%2A%28sqrt%283%29%29=sqrt%289%29=3.


%28highlight%28sqrt%283%29%29%2Bsqrt%282%29%29%28sqrt%283%29%2Bhighlight%28sqrt%282%29%29%29 Multiply the Outer terms:%28sqrt%283%29%29%2A%28sqrt%282%29%29=sqrt%286%29.


%28sqrt%283%29%2Bhighlight%28sqrt%282%29%29%29%28highlight%28sqrt%283%29%29%2Bsqrt%282%29%29 Multiply the Inner terms:%28sqrt%282%29%29%2A%28sqrt%283%29%29=sqrt%286%29.


%28sqrt%283%29%2Bhighlight%28sqrt%282%29%29%29%28sqrt%283%29%2Bhighlight%28sqrt%282%29%29%29 Multiply the Last terms:%28sqrt%282%29%29%2A%28sqrt%282%29%29=sqrt%284%29=2.


---------------------------------------------------


3%2Bsqrt%286%29%2Bsqrt%286%29%2B2 Now collect every term to make a single expression.


5%2B2%2Asqrt%286%29 Now combine like terms.


So %28sqrt%283%29%2Bsqrt%282%29%29%5E2 FOILs to 5%2B2%2Asqrt%286%29.


In other words, %28sqrt%283%29%2Bsqrt%282%29%29%5E2=5%2B2%2Asqrt%286%29.