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Multiplying roots

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Source: — Problem Solving |
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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?


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