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.

Guest Aug 5, 2022

#1**0 **

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

Guest Aug 5, 2022

edited by
Guest
Aug 5, 2022

#3**+1 **

That logic is incorrect because they have different denominators. In the first fraction b is \(\sqrt{21}\) and in the second it is \(\sqrt {14}\)

BuilderBoi
Aug 5, 2022