GMAT Prep radical expression

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oex85: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sat Jun 25, 2011 8:49 am

by oex85 » Thu Sep 01, 2011 8:05 am

[ âˆš(9+âˆš80)+âˆš(9-âˆš80) ]^2

A. 1
B. 9 - 4sqrt5
C. 18 - 4sqrt5
D. 18
E. 20

Clearly, there's some small (yet v important!)detail I'm missing.

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Source: Beat The GMAT — Problem Solving | Thu Sep 01, 2011 8:05 am

oex85: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sat Jun 25, 2011 8:49 am

by oex85 » Thu Sep 01, 2011 8:16 am

Sorry! Found old threads with good answers after searching again...

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by Anurag@Gurome » Thu Sep 01, 2011 8:41 am

Take, âˆš(9 + âˆš80) = a and âˆš(9 - âˆš80) = b
Hence, we need to find the value of (a + b)Â² = aÂ² + 2ab bÂ²

aÂ² = [âˆš(9 + âˆš80)]Â² = (9 + âˆš80)
bÂ² = [âˆš(9 - âˆš80)]Â² = (9 - âˆš80)
ab = [âˆš(9 - âˆš80)]*[âˆš(9 - âˆš80)] = âˆš[(9 - âˆš80)(9 - âˆš80)] = 9Â² - (âˆš80)Â² = 81 - 80 = 1

Thus, aÂ² + bÂ²= (9 + âˆš80) + (9 - âˆš80) = 18

Hence, (a + b)Â² = aÂ² + 2ab bÂ² = 18 + 2 = 20

The correct answer is E.

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