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Rationalize the denominator of 5/(3 - sqrt(3)), and write your answer in the form (A + B*sqrt(3))/C where the fraction is in lowest terms. What is A + B + C?

 Dec 31, 2020
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Rationalize the denominator of 5/(3 - sqrt(3)), and write your answer in the form (A + B*sqrt(3))/C where the fraction is in lowest terms. What is A + B + C?     

 

Multiply both the numerator and

the denominator by (3 + sqrt(3)) 

This gets the radical out of the

denominator. 

 

         5                (3 + sqrt(3))  

——————  •  ——————  

(3 – sqrt(3))        (3 + sqrt(3))  

 

 

5 • (3 + sqrt(3))         15 + (5 • sqrt(3)  

———————   =   ———————  

      9 – 3                             6  

 

So the answer to "What is (A + B + C)?" is (15 + 5 + 6) which totals 26.  

.

 Dec 31, 2020

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