We have to find between which integers is located in the square root of 138.
If we calculate 11^2 we have 121.
As 121 < 138, the square root of 138 is then bigger than 11.
If we calculate 12^2, we have 144.
As 144 > 138, the square root of 138 is smaller than 12.
So, the square root of 138 has to be between 11 and 12.