SOLUTION: Hi, I am trying to do this two problems, and I am lost. Could some one please help me. I would like to thank you for the time you have spend to help me . Perform the indicated

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, I am trying to do this two problems, and I am lost. Could some one please help me. I would like to thank you for the time you have spend to help me . Perform the indicated      Log On


   

Question 140490: Hi, I am trying to do this two problems, and I am lost. Could some one please help me. I would like to thank you for the time you have spend to help me .
Perform the indicated operations:
2√[48] + 7√[12] –√[27]
Rationalize the denominator:
___ 2____
√[3] + √[2]
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Perform the indicated operations:
2√[48] + 7√[12] –√[27]
:
Factor the values inside the radicals to reveal the perfect squares:
2sqrt%2816%2A3%29 + 7sqrt%284%2A3%29 - sqrt%289%2A3%29
Extract the square root of those perfect squares:
2%2A4sqrt%283%29 + 7%2A2sqrt%283%29 - 3sqrt%283%29
which is:
8sqrt%283%29 + 14sqrt%283%29 - 3sqrt%283%29
These are like terms, just do the math and you have:
19sqrt%283%29
:
:
Rationalize the denominator:
___ 2____
√[3] + √[2]
:
2%2F%28sqrt%283%29%2Bsqrt%282%29%29
multiply equation by the conjugate of the denominator: (any expression over itself = 1)
2%2F%28sqrt%283%29%2Bsqrt%282%29%29 * %28sqrt%283%29-sqrt%282%29%29%2F%28sqrt%283%29-sqrt%282%29%29 = %282sqrt%283%29-2sqrt%282%29%29%2F%283+-+2%29 = %282sqrt%283%29-2sqrt%282%29%29%2F1 = 2sqrt%283%29-2sqrt%282%29
:
Note that the when you FOIL the denominators, the middle terms cancel!