2007 Alabama ARML TST Problems/Problem 1

Problem

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

Solution

$\sqrt{2000(2000+7)(2000+8)(2000+15)+784}$

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

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

$=2000^2+15\cdot 2000+28=\boxed{4030028}$

See also

2007 Alabama ARML TST (Problems)
Preceded by:
First Question
Followed by:
Problem 2
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