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2007 Alabama ARML TST Problems/Problem 1

Revision as of 12:18, 17 June 2008 by 1=2 (talk | contribs) (New page: ==Problem== Compute: <math>\sqrt{2000\cdot 2007\cdot 2008\cdot 2015+784}.</math> ==Solution== <math>2000(2000+7)(2000+8)(2000+15)+784=(2000^2+15\cdot 2000+56)(2000^2+15\cdot 2000)+28^2=(2...)
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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 $$ (Error compiling LaTeX. Unknown error_msg)\sqrt{2000\cdot 2007\cdot 2008\cdot 2015+784}=\boxed{4030028}$

See also

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