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root[3*root{80}+3/(9+4*root{5})]=?

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root[3*root{80}+3/(9+4*root{5})]=? [#permalink] New post 26 Jan 2012, 05:30
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\sqrt{3*\sqrt{80}+\frac{3}{9+4*\sqrt{5}}}=?

A) \sqrt{3*\sqrt{5}}

B) 3

C) 3*\sqrt{3}

D) 3+2*\sqrt{5}

E) 9+4*\sqrt{5}
[Reveal] Spoiler: OA
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Re: Sqaure Root [#permalink] New post 26 Jan 2012, 05:59
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LM wrote:
\sqrt{3*\sqrt{80}+\frac{3}{9+4*\sqrt{5}}}=?

A) \sqrt{3*\sqrt{5}}

B) 3

C) 3*\sqrt{3}

D) 3+2*\sqrt{5}

E) 9+4*\sqrt{5}


\sqrt{3\sqrt{80}+\frac{3}{9+4\sqrt{5}}}=\sqrt{12\sqrt{5}+\frac{3}{9+4\sqrt{5}}*\frac{9-4\sqrt{5}}{9-4\sqrt{5}}}=\sqrt{12\sqrt{5}+\frac{3(9-4\sqrt{5})}{81-80}}=\sqrt{12\sqrt{5}+27-12\sqrt{5}}=\sqrt{27}=3\sqrt{3}.

Answer: C.
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Re: Sqaure Root [#permalink] New post 26 Jan 2012, 06:00
By taking reciprocals we can solve this question. Ans is C
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Re: root[3*root{80}+3/(9+4*root{5})]=? [#permalink] New post 12 Aug 2012, 08:56
Thanks Bunuel -- You Are The Man!! :)
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Re: root[3*root{80}+3/(9+4*root{5})]=? [#permalink] New post 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.
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Re: root[3*root{80}+3/(9+4*root{5})]=? [#permalink] New post 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.
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Que from MGMAT - [#permalink] New post 07 Apr 2013, 09:59
Hi,

I was going through MGMAT CAT and found the below question.

{(80)^1/3 + 3 /(9 + 4 (5)^1/2)}^1/2



Answer C): 3 (3)^1/2

I am unable to figure out how the answer is coming. Could anyone please help me with this. (Attached the solution as a image)


I couldn't post other options as the page is blurred.
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Re: Que from MGMAT - [#permalink] New post 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
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Re: Que from MGMAT - [#permalink] New post 07 Apr 2013, 21:36
Expert's post
saratchandra wrote:
Hi,

I was going through MGMAT CAT and found the below question.

{(80)^1/3 + 3 /(9 + 4 (5)^1/2)}^1/2



Answer C): 3 (3)^1/2

I am unable to figure out how the answer is coming. Could anyone please help me with this. (Attached the solution as a image)


I couldn't post other options as the page is blurred.


Merging similar topics. Please refer to the solution above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Que from MGMAT - [#permalink] New post 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...
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Re: Que from MGMAT - [#permalink] New post 14 Apr 2013, 07:17
Bunuel wrote:
saratchandra wrote:
Hi,

I was going through MGMAT CAT and found the below question.

{(80)^1/3 + 3 /(9 + 4 (5)^1/2)}^1/2



Answer C): 3 (3)^1/2

I am unable to figure out how the answer is coming. Could anyone please help me with this. (Attached the solution as a image)


I couldn't post other options as the page is blurred.


Merging similar topics. Please refer to the solution above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html



thanks for merging with the old thread.. i couldn't understand how to search, so posted it. I will try to avoid that in future
Re: Que from MGMAT -   [#permalink] 14 Apr 2013, 07:17
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