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.
if a/b = sqrt10/sqrt21 then a =sqrt10
if b/c = sqrt14/sqrt15 then c = sqrt15
then a/c = sqrt10/sqrt15
rationalize the denominator means no sqrt in the denominator
to rationalize it, multiply by 1 using the denominator/denominator as our 1
sqrt10/sqrt15 * Sqrt15/sqrt15
sqrt10*sqrt15/sqrt15*sqrt15
sqrt150/15
5sqrt6/15
sqrt6/3
+2666 That logic is incorrect because they have different denominators. In the first fraction b is \(\sqrt{21}\) and in the second it is \(\sqrt {14}\)
