A rational number is a any number that can be written as a fraction with integers
The first option is a number with a repeating decimal.
[tex]1.\bar{14}[/tex]
Numbers with repeating decimals are rational numbers
Hence, it is a rational number
The second option is a surd
[tex]\sqrt[]{5}[/tex]
It has an irrational root of a rational number and its decimal function is continuous without a recuring pattern.
Hence, the second option is an irrational number
The third option
[tex]\sqrt[]{16}=4[/tex]
The value of the square root of 16 is 4 which can be expressed as a ratio of two numbers
Hence, it is a rational number
The fourth option is the ratio of two integers
[tex]\frac{6}{7}[/tex]
Hence, it is a rationl number
The fifth option is a number with a continuous decimal and without a recuring pattern
Hence, it is an irrational number
Hence, the list of rational numbers given is
[tex]\begin{gathered} 1.\bar{14} \\ \sqrt[]{16} \\ \frac{6}{7} \end{gathered}[/tex]
