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This can be solved by taking the denominator as 9+4\sqrt{5} and then taking this as the common factor. We get the the ans as C.
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I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

This kind of problems always seemed to me very scary and requires a lot of calculation, but later i realised that GMAT never asks something that you need to calculate a lot, so one needs to look for some pattern or similar numbers/sets. In our case, we look at denominator 9+\sqrt{5} and 3\sqrt{80}, so 80 is 2^4*5, which means 4\sqrt{5}, from here we feel that numerator and denominator could be reduced. The rest is just calculations. In my opinion the most crucial part is this one.
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Lets analyze the first part \(3\sqrt{80} = 3\sqrt{5*16} = 3*4\sqrt{5}\) The second term: Denominator \((9+4\sqrt{5})*(9-4\sqrt{5})=9^2-4^2*5=1\) Rule: (x+y)(x-y)=x^2-y^2 The second term: Numerator \(3*(9-4\sqrt{5})=27-12\sqrt{5}\) Now putting all in one: \(\sqrt{(}12\sqrt{5}+27-12\sqrt{5})=\) \(\sqrt{27}=\sqrt{3*3^2}=3\sqrt{3}\)

Hope it's clear now
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It is beyond a doubt that all our knowledge that begins with experience.

Lets analyze the first part \(3\sqrt{80} = 3\sqrt{5*16} = 3*4\sqrt{5}\) The second term: Denominator \((9+4\sqrt{5})*(9-4\sqrt{5})=9^2-4^2*5=1\) Rule: (x+y)(x-y)=x^2-y^2 The second term: Numerator \(3*(9-4\sqrt{5})=27-12\sqrt{5}\) Now putting all in one: \(\sqrt{(}12\sqrt{5}+27-12\sqrt{5})=\) \(\sqrt{27}=\sqrt{3*3^2}=3\sqrt{3}\)

Hope it's clear now

thank you!! .. that 3 is so small that i took cube root 80...

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Though, I am quite comfortable with the method mentioned by Bunuel, I found an alternative way by The Economist.

\(9 + 4*\sqrt{5}\) will be approx. equal to 9 + 4 x 2 = 17. Hence 3/ 17 will be quite less to contribute towards the value of expression.

\(3\sqrt{80}\) is approx. 3 x 9 = 27. now \(\sqrt{27}\) will be something more than 5.

Now coming to options:

(A)\(\sqrt{3*\sqrt{5}}\) is approx \(\sqrt{6}\) which is quite less than 5. Rejected. (B) Rejected. (C) 3 x 1.732 = 5.1 , which is in our desired range. (D) 3 + 4 =7. Rejected (E) 9 + 4 x 2 = 17. Rejected.

Hence the correct ans is (C).

If you like this Ballparking method, please press "Kudos".

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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