Getting to the Root of Things

Can you simplify the following expression into a rational number? If you can, then do it.

√(1+1000000√(1+1000001√(1+1000002√(1+1000003√(1+1000004√(1+…)) ) ) ) )

Know the answer? Send your solution to

Cross Every Doorway Once

Many solutions were received. Here is one by Shyam Bihari Agarwal.

Solutions were also submitted by Jordan C. Bonner, Roger Bovard, Paul Chabarek, Al Commodore, Bob Conger, Akshar Gohil, Luc Langlois, Jerry Miccolis, Christina Negley, Gregory Scruton, Betty-Jo Walke, David Uhland and David Vogt.