let the 3 consecutive even numbers be:

2x - 2, 2x and 2x + 2, where x is integer

2 times the square root of the sum of 3 consecutive even numbers is 24:

2(√(2x - 2 + 2x + 2x + 2)) = 24

2√(6x) = 24 divide both sides by 2

√(6x) = 12

6x = 12^2

x = 144/6

x = 24

the 3 consecutive even numbers are:

2*24 - 2 = 46

2*24 = 48

2*24 + 2 = 50.