Question

1. which of the following is an irrational number?

f (\frac{5}{9})
g (sqrt{81})
h (4)
j (sqrt{2})

Explanation:

Step1: Analyze Option F

The number $\frac{2}{7}$ is a fraction of two integers (2 and 7, where 7 ≠ 0), so it is a rational number.

Step2: Analyze Option G

Calculate $\sqrt{81}$. Since $9\times9 = 81$, we have $\sqrt{81}=9$, which is an integer and thus a rational number.

Step3: Analyze Option H

The number 4 is an integer, and all integers are rational numbers.

Step4: Analyze Option J

The number $\sqrt{2}$ is a well - known irrational number. Its decimal expansion is non - repeating and non - terminating, and it cannot be expressed as a fraction of two integers.

Answer:

J. $\sqrt{2}$