Solution:

111111111

Explanation:

It's a maths magical square root series as :

Square root of number 121 is 11

Square root of number 12321 is 111

Square root of number 1234321 is 1111

Square root of number 123454321 is 11111

Square root of number ********** is 111111

Square root of number 1234567654321 is 1111111

Square root of number 123456787654321 is 11111111

Square root of number 12345678987654321 is 111111111 (answer)