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Multiplying roots

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by sgarnepudi » Sun Sep 12, 2010 9:33 am
I could solve it in less than 3 min even thru traditional way.

expand as (a+b)^2

(9+sqrt(80))+(9-sqrt(80))+2(sqrt(9+sqrt(80)))(sqrt(9-sqrt(80)))

=> 9+9+2(sqrt(9+sqrt(80))(9-sqrt(80))) the last part is (a+b)(a-b)

=> 18+2(sqrt(9^2-80))

=> 18+2(1)

=>20
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by diebeatsthegmat » Sun Sep 12, 2010 9:37 am
1uponGMAT wrote:This is a problem that I had a tough time solving under 3 minutes. Any advice on how to solve it, and maybe a shortcut?


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just do it normally
first of all used (a+b)^2=a^2+b^2+2ab then
use a^2-b^2 for the 2ab you wll get the right answer
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by 1uponGMAT » Sun Sep 12, 2010 9:46 am
for the a^2 + b^2 I get:
9 + root(80) + 9 - root(80) = 18

for the 2ab I get:
2*(9 + root(80) + 9 - root(80)) = 2 * 18

= 54

which is wrong
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by Brian@VeritasPrep » Mon Sep 13, 2010 10:51 am
Hey guys,

I just posted this weekend on a nearly-identical question on the Math forum:

https://www.beatthegmat.com/square-root- ... 65835.html

That explanation should explain all of the steps, just with different numbers.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep

Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
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