Step 1: sqrt(50) = sqrt(25*2) = 5*sqrt(2). Step 2: sqrt(2) is irrational, so 5*sqrt(2) is irrational. Step 3: 0.125 = 1/8 (rational). Step 4: -2/7 is rational. Step 5: 0.333... repeating equals 1/3 (rational). Therefore the irrational choice is sqrt(50).

Step 1: Natural numbers are 1, 2, 3, ... and do not include negative numbers. Step 2: Whole numbers are 0, 1, 2, 3, ... and do not include negatives. Step 3: Integers include ..., -2, -1, 0, 1, 2, ... so -7 is an integer. Step 4: Irrational numbers cannot be written as a/b; -7 is rational but the best classification among the options is Integers.