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2007 Alabama ARML TST Problems/Problem 1

Revision as of 12:19, 17 June 2008 by 1=2 (talk | contribs)

Problem

Compute: $\sqrt{2000\cdot 2007\cdot 2008\cdot 2015+784}.$

Solution

$2000(2000+7)(2000+8)(2000+15)+784$

$=(2000^2+15\cdot 2000+56)(2000^2+15\cdot 2000)+28^2$

$=(2000^2+15\cdot 2000+28)(2000^2+15\cdot 2000+28)-28^2+28^2$

Thus $\sqrt{2000\cdot 2007\cdot 2008\cdot 2015+784}=\boxed{4030028}$

See also

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