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Re: root[3*root{80}+3/(9+4*root{5})]=? [#permalink]
12 Aug 2012, 10:29

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. _________________

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+

Re: root[3*root{80}+3/(9+4*root{5})]=? [#permalink]
16 Aug 2012, 22:16

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. _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: Que from MGMAT - [#permalink]
07 Apr 2013, 10:07

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 _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Que from MGMAT - [#permalink]
14 Apr 2013, 07:16

Zarrolou wrote:

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...

Re: root[3*root{80}+3/(9+4*root{5})]=? [#permalink]
29 Dec 2014, 23:22

Hello from the GMAT Club BumpBot!

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. _________________

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".

My last interview took place at the Johnson School of Management at Cornell University. Since it was my final interview, I had my answers to the general interview questions...