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?
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.
.