根号（1999*2000*2001*2002+1）化简

=根号(1999*2000*2001*2002+1]
=根号[(2000-1)*2000*(2000+1)*(2000+2)+1]
=根号[2000*(2000+1)*(2000-1)*(2000+2)+1]
=根号[(2000^2+2000)*(2000^2+2000*2-2000*1-2)+1]
=根号[(2000^2+2000)*(2000^2+2000-2)+1]
=根号[(2000^2+1999+1)*(2000^2+1999-1)+1]
=根号{[(2000^2+1999)+1]*[(2000^2+1999)-1]+1}
=根号{[(2000^2+1999)^2-1]+1}
=根号{(2000^2+1999)^2-1+1}
=根号{(2000^2+1999)^2}
=2000^2+1999
=4001999

根号（1999*2000*2001*2002+1）
=根号[(2000-1)*2000*2001*(2001+1)+1]
=根号[2000*2001(2000*2001-2)+1]
=根号[(2000*2001)²-2*(2000*2001)+1]
=根号(2000*2001-1)²
=2000*2001-1
=4002000-1
=4001999