Difference between revisions of "2007 Alabama ARML TST Problems/Problem 1"
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==Solution== | ==Solution== | ||
| − | < | + | <cmath>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</cmath> |
| − | Thus <math>\sqrt{2000\cdot 2007\cdot 2008\cdot 2015+784}=\boxed{4030028} | + | Thus <math></math>\sqrt{2000\cdot 2007\cdot 2008\cdot 2015+784}=\boxed{4030028}$ |
==See also== | ==See also== | ||
Revision as of 13:18, 17 June 2008
Problem
Compute: 
Solution
![\[2000(2000+7)(2000+8)(2000+15)+784=(2000^2+15\cdot 2000+56)(2000^2+15\cdot 2000)+28^2=(2000^2+15\cdot 2000+28)(2000^2+15\cdot 2000+28)-28^2+28^2\]](http://latex.artofproblemsolving.com/6/6/1/66154320997e62989142bf6c2699ed3add35e1f1.png)
Thus $$ (Error compiling LaTeX. Unknown error_msg)\sqrt{2000\cdot 2007\cdot 2008\cdot 2015+784}=\boxed{4030028}$
