（根号下2000×2001×2002×2003+1）-2000²
=√[2001×2002×(2001-1)×(2002+1)+1]-2000²
=√[2001×2002×(2001×2002-2002+2001-1)+1]-2000²
=√[2001×2002×(2001×2002-2)+1]-2000²
=√[(2001×2002)²-2×(2001×2002)+1]-2000²
=√(2001×2002-1)²-2000²
=2001×2002-1-2000²
=(2000+1)×2002-2000²-1
=2000×(2002-2000)+2002-1
=4000+2001
=6001