Question

which of the following is a rational number?\
\\(\sqrt{5}\\) \\(\sqrt{8}\\) 8.66 \\(\pi\\)

Explanation:

Step1: Recall the definition of rational numbers

A rational number is a number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. This includes integers, fractions, terminating decimals, and repeating decimals. Irrational numbers are numbers that cannot be expressed as such a fraction, like non - perfect square roots and $\pi$.

Step2: Analyze $\sqrt{5}$

$\sqrt{5}\approx2.23607\cdots$, and it is a non - repeating, non - terminating decimal. Also, 5 is not a perfect square, so $\sqrt{5}$ is an irrational number.

Step3: Analyze $\sqrt{8}$

Simplify $\sqrt{8}=\sqrt{4\times2} = 2\sqrt{2}\approx2\times1.4142 = 2.8284\cdots$, which is a non - repeating, non - terminating decimal. Since 8 is not a perfect square, $\sqrt{8}$ is an irrational number.

Step4: Analyze $8.66$

$8.66$ is a terminating decimal. A terminating decimal can be written as a fraction. For example, $8.66=\frac{866}{100}=\frac{433}{50}$, where 433 and 50 are integers and $50
eq0$. So $8.66$ is a rational number.

Step5: Analyze $\pi$

$\pi\approx3.1415926535\cdots$ is a non - repeating, non - terminating decimal, so $\pi$ is an irrational number.

Answer:

$8.66$ (the option with the number $8.66$)