SOLUTION: Can you help me with rationalizing the denominator on the following: 5 on the top, fraction bar, 9 minus radical sign 3 on the bottom (the 3 is under the radical sign)

Question 64287: Can you help me with rationalizing the denominator on the following:
5 on the top, fraction bar, 9 minus radical sign 3 on the bottom (the 3 is under the radical sign)
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
To simplify: (5)/(9-sqrt(3))
First, we want to get rid of the radical in the denominator. We do this by multiplying the factor (9-sqrt(3)) by its conjugate (9+sqrt(3)). when we do this we get:
(5)/(81-9sqrt3+9sqrt3-3) or
(5)/(81-3) simplifying, we have:
5/78
Note: If the original factor is (a+b), the conjugate of (a+b) is defined as the factor that, when multiplied by the original factor, yields the answer (a^2-b^2) and that factor is (a-b)--a powerful tool for simplifying radicals and complex numbers.
Hope this helps. Have a nice holiday season---ptaylor

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