1) Considering that Rational numbers are all numbers that can be written as a ratio (fraction) a/b and Irrational the ones that can not be written as a ratio. Let's examine
Among the numbers
9.68 is a repeating number = 9.6888888.. and every repeating number can be rewritten as a ratio.
2.010010001... does not have a period, since this part after the dot:
2.010010001...is getting larger and larger and therefore that's a non-periodic (no repeating number(s)) and an irrational number
√64= 8 and 8 can be written as 8/1 so that's a rational number.
-51/5 = is already a ratio, then it is a rational number
√6 = is 2.449489749... and infinite a non-periodic number, so that's an irrational number. √6 does not have an exact root.
In short, infinite non-periodic numbers are irrational, like π, √6, √2, etc.
All of the others including the infinite periodic numbers are rational ones like 2, √64, -51/5,