## Sum of Squares

The eighteenth-century mathematician Joseph Louis Lagrange proved that every positive integer is the sum of, at most, four squares. Find at least one way to write $2008$ as the sum of three squares.
Source: NCTM Mathematics Teacher 2008

SOLUTION
$\sqrt{2008}=44.81$
$2008-44^2=72$
$\sqrt{72}=8.49$
$2008-44^2-8^2=8$
$2008=44^2+8^2+2^2+2^2$ a sum of four squares
We want a sum of three squares, so we try $7^2,6^2$, etc.
$2008-44^2-7^2=23$ not a perfect square
$2008-44^2-6^2=36$
$2008=44^2+6^2+6^2$
Continuing in this slow and tedious fashion we will find $3$ more solutions
$2008=42^2+12^2+10^2$
$2008=36^2+26^2+6^2$
$2008=30^2+28^2+18^2$

$44^2+6^2+6^2$
$42^2+12^2+10^2$
$36^2+26^2+6^2$
$30^2+28^2+18^2$