Question

Which of the numbers from the list are rational? Choose ALL that are correct.

Answer 1

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.

`1.\bar{14}`

Numbers with repeating decimals are rational numbers

Hence, it is a rational number

The second option is a surd

`\sqrt[]{5}`

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

`\sqrt[]{16}=4`

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

`(6)/(7)`

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

`\begin{gathered} 1.\bar{14} \\ \sqrt[]{16} \\ (6)/(7) \end{gathered}`