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GMAT prep simple ques

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Source: — Problem Solving |

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by Anurag@Gurome » Wed Mar 14, 2012 7:57 pm
jkelk wrote:Hi

Please help solve the attached.

Thanks,
J
Apply the formula, (a + b)² = a² + b² + 2ab

[√(9 + √80) + √(9 - √80)]² = [√(9 + √80)]² + [√(9 - √80)]² + 2√(9 + √80)√(9 - √80)
= 9 + √80 + 9 - √80 + 2(81 - 80)
= 18 + 2
= 20

The correct answer is E.
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by jkelk » Thu Mar 15, 2012 7:55 am
Hi Anurag,

Thanks for replying, could you please explain how you simplified 2√(9 + √80)√(9 - √80)
I seem to be missing this part.

Thanks,
J
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by Anurag@Gurome » Thu Mar 15, 2012 8:10 pm
jkelk wrote:Hi Anurag,

Thanks for replying, could you please explain how you simplified 2√(9 + √80)√(9 - √80)
I seem to be missing this part.

Thanks,
J
Apply the formula, (a + b)(a - b) = a² - b²
2√(9 + √80)√(9 - √80) = 2√{(9 + √80)(9 - √80)}
= 2√{9² - (√80)²}
= 2√(81 - 80)
= 2√1
= 2

I hope it helps.
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