Explanation:
sqrt(50) - irrational. sqrt(50) = sqrt(25×2) = 5×sqrt(2).
sqrt(2) is the prime example of an irrational number (infinite positions after the decimal point, no repeating patterns).
3.45656565656... - rational. although it is infinite, it has had a repeating pattern that allows us to write it as fraction.
0 - rational. as every integer or whole number.
sqrt(4/9) = 2/3 - rational as expressed as fraction.
0.38 - rational. it is a finite decimal number, and can be easily expressed as fraction (like 38/100).
sqrt(81) = 9 - rational. again, as every integer or whole number.
2pi - irrational. pi is a prime example of an irrational number (infinite and no repeating pattern). not possible to write as fraction. Any combination of pi is also irrational.
sqrt(1.69) = 1.3 - rational. finite decimal that we can easily write also as fraction (like 13/10).
sqrt(2/9) = sqrt(2)/3 - irrational, as sqrt(2) is a prime example for an irrational number. any combination with an irrational number is an irrational number.