99…9(1000个9)×99…9(1000个9)+199…9(1000个9)=?

√[99…9(n个9)×99…9(n个9)+199…9(n个9)]
=√{[99…9(n个9)]^2+2*[99…9(n个9)]+1}
=√{[99…9(n个9)+1]^2}
=√{[100...0(n个0)]^2}
=√[(10^n)^2]
=10^n.
99…9(1000个9)×99…9(1000个9)+199…9(1000个9)
=[99…9(1000个9)]^2+2*99…9(1000个9)+1
=[99…9(1000个9)+1]^2
=[100...0(1000个0)]^2
=(10^1000)^2
=10^2000.