Radical with pattern Let $a =111 \ldots 1$, where the digit $1$ appears $2018$ consecutive times.
Let $b = 222 \ldots 2$, where the digit $2$ appears $1009$ consecutive times.
Without using a calculator, evaluate $\sqrt{a − b}$.

\begin{align}
  a &= \frac{10^{2018}-1}{9} \\
  b &= \frac{2(10^{1009}-1)}{9} \\
  a-b &= \frac{10^{2018}-2\times10^{1009}+1}{9} \\
  &= \frac{(10^{1009}-1)^{2}}{9} \\
\end{align}
Can you proceed?
