Difference between revisions of "2007 Alabama ARML TST Problems/Problem 1"

Revision as of 12:20, 17 June 2008

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

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

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

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

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

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	==See also==		==See also==
		+	{{ARML box\|year=2007\|state=Alabama\|before=First Question\|num-a=2}}