The simplest way is to solve 4n + 6 = 138 for the smallest of them.
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The integers are 44, 46 and 48.
Do-it-in-your-head method: The middle number MUST be a third of the total so 138 divided by 3 is 46, making your three numbers 44, 46 and 48. Shazam!
The numbers are 45, 46 and 47.
The sets are 277, 279 and 136, 138, 140, 142.
The square root of 138 is approximately 11.747. So, the two consecutive whole numbers between which the square root of 138 lies are 11 and 12. This is because 11^2 is 121, which is less than 138, and 12^2 is 144, which is greater than 138.