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 [imath]x = 7000[/imath], then we have:

[imath]\sqrt{(x-3)(x-1)(x+1)(x+3)+16}[/imath]

[imath]\sqrt{(x^2-9)(x^2-1)+16}[/imath]

[imath]\sqrt{x^4-10x^2+25}[/imath]

[imath]\sqrt{(x^2-5)^2}[/imath]

[imath]7000^2-5[/imath]

 

[lookagain]

Spoiler

[imath]7000^2-5 = \ ?[/imath]

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

[imath]49000-5 = 48995[/imath]

Spoiler

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