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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.

 Aug 5, 2022
 #1
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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

 Aug 5, 2022
edited by Guest  Aug 5, 2022
 #3
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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
 #2
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https://web2.0calc.com/questions/algebra_96607

 Aug 5, 2022

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