+421 Look for patterns!
$$99 \cdot 99=9801$$
$$ 999 \cdot 999 = 998001$$
When looking at the patterns, we see that the formula for the square a number consisting of $n$ $9's$ is:
Number of 9s in the number = Add $n-1$ 9s
Then add an 8
Number of 0s in the number = Add $n-1$ 0s
Then add a 1.
There are 16 digits in the number $999999999999999999.$ So, $$\boxed{999999999999999999^2 = 999999999999999998000000000000000001}$$
