SOLUTION: Express sqrt3/ 6-sqrt3 in the form p+q(sqrt3) where p and q are rational I have this exercise and I have no idea how to solve it Could you please help me? The chapter is call

Algebra ->  Square-cubic-other-roots -> SOLUTION: Express sqrt3/ 6-sqrt3 in the form p+q(sqrt3) where p and q are rational I have this exercise and I have no idea how to solve it Could you please help me? The chapter is call      Log On


   

Question 1091826: Express sqrt3/ 6-sqrt3 in the form p+q(sqrt3) where p and q are rational
I have this exercise and I have no idea how to solve it
Could you please help me?
The chapter is called surds
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Express sqrt3/ 6-sqrt3 in the form p+q(sqrt3) where p and q are rational
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You have to make the DEN rational, get rid of the radical.
Multiply NUM and DEN by the conjugate of the DEN, 6+sqrt(3)
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sqrt%283%29%2F%286-sqrt%283%29%29
= sqrt%283%29%2A%286%2Bsqrt%283%29%29%2F%28%286-sqrt%283%29%29%2A%286%2Bsqrt%283%29%29%29
= %286sqrt%283%29+%2B+3%29%2F%2836+-+3%29
= %286sqrt%283%29+%2B+3%29%2F33
= %282sqrt%283%29+%2B+1%29%2F11
= %281%2F11%29+%2B+%282%2F11%29%2Asqrt%283%29
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PS Use parentheses.
Express sqrt3/ 6-sqrt3 ----> Express sqrt3/(6-sqrt3)