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\sqrt{4002000\times 2002\times 2003+1}
Multiply 2000 and 2001 to get 4002000.
\sqrt{8012004000\times 2003+1}
Multiply 4002000 and 2002 to get 8012004000.
\sqrt{16048044012000+1}
Multiply 8012004000 and 2003 to get 16048044012000.
\sqrt{16048044012001}
Add 16048044012000 and 1 to get 16048044012001.
4006001
Calculate the square root of 16048044012001 and get 4006001.