Simplifying arithmetical/radical expression: sqrt(6997*6999*7001*7003 + 16)

[lookagain]

Without using a calculator or computer, please write down the steps for simplifying the following expression (using spoilers):

$\displaystyle \sqrt{6,997 \cdot 6,999 \cdot 7,001 \cdot7,003 \ + \ 16 \ }$

 

[BigBeachBanana]

Spoiler

Let $x = 7000$, then we have:

$\sqrt{(x-3)(x-1)(x+1)(x+3)+16}$

$\sqrt{(x^2-9)(x^2-1)+16}$

$\sqrt{x^4-10x^2+25}$

$\sqrt{(x^2-5)^2}$

$7000^2-5$

 

[lookagain]

Spoiler

$7000^2-5 = \ ?$

That's almost everything except the final answer, that is, stopping short.
I had to click your post #2 as a "Like" because of the correct process you supplied.

 

[lookagain]

Spoiler

$49000-5 = 48995$

Spoiler

$\displaystyle 7,000^2 - 5 \ = \ 49,000,000 - 5 \ = \ 48,999,995$