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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).
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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".
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