Can you find the square root of 12345678987654321?

$\begin{array} {rccc} & \underbrace{1^2}_{\text{No. of 1's } = \color{#D61F06}1} & = & \color{#D61F06} 1 \\ & \underbrace{11^2}_{\text{No. of 1's }= \color{#D61F06}2} & = & 1{\color{#D61F06}2}1 \\ & \underbrace{111^2}_{\text{No. of 1's }= \color{#D61F06}3} & = & 12{\color{#D61F06}3}21 \\ & \underbrace{1111^2}_{\text{No. of 1's }= \color{#D61F06}4} & = & 123{\color{#D61F06}4}321 \\ \implies & \underbrace{111 \cdots 111^2}_{\text{No. of 1's }= \color{#D61F06}n} & = & 123\cdots {\color{#D61F06}n}\cdots321 \\ \implies & \underbrace{111\ 111\ 111^2}_{\text{No. of 1's }= \color{#D61F06}9} & = & 12345678{\color{#D61F06}9}87654321 \end{array}$

Therefore, $\sqrt{12345678987654321} = \boxed{111\ 111\ 111}$ .