Evaluate √((1000000)(1000001)(1000002)(1000003)+1)

Evaluate $\sqrt{(1000000)(1000001)(1000002)(1000003)+1}$ without the help of calculator.

At first glance, you might notice $1000000,\,1000001,\,1000002,\,1000003$ are the terms from arithmetic sequence and now, we have to compute the product of these four figures, but not to find the sum of the first four terms from that sequence.

But, let us look at it a lot more closely, we can actually now discern a pattern if we employ the heuristic strategy by using the substitution method which helps in solving this intriguing problem.