Suppose that a, b, and c are real numbers such that a/b = sqrt(10)/sqrt(21) and b/c = sqrt(14)/sqrt(15). Find a/c. Completely simplify and rationalize the denominator.
(a/b)*(b/c) = √10/√15. If we rationalize that, we get √150/15, which is 5√6/15, which is √6/3
+129850 a/b = sqrt (10) / sqrt (21)
a = b sqrt (10) /sqrt (21)
b/c = sqrt (14) / sqrt (15)
c/b = sqrt (15) / sqrt (14)
c = b sqrt (15) / sqrt (14)
a / c = [ bsqrt (10) / sqrt (21)] / [ bsqrt (15)/sqrt (14) ] =
[sqrt (10) sqrt (14)] / [ sqrt (21) sqrt (15)] =
sqrt (10) / sqrt (15) * sqrt (14) / sqrt (21) =
sqrt (10/15) * sqrt ( 14/21) =
sqrt (2/3) * sqrt (2/3) =
2/3
