31 is between the square numbers 25 and 36, whose respective square-roots are 5 and 6. Lets take the median of 25 and 36 to see how far in the middle 31 is.
(25 + 36) / 2 = 61 / 2 = 30.5
This is close to 31.
Take the median of the square-roots.
(5 + 6) / 2 = 11 / 2 = 5.5 This is the median square-root.
Square-root of 31 is between 5.5 and 6.
√31 = 5.55
