Question

which of the following is a rational number? \\(\frac{21}{19}\\) \\(sqrt{2}\\) \\(sqrt{55}\\) \\(pi\\)

Explanation:

Step 1: Recall the definition of a rational number

A rational number is a number that can be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q
eq0$. It can be a fraction, a terminating decimal, or a repeating decimal. Irrational numbers cannot be expressed as such and have non - repeating, non - terminating decimal expansions. Square roots of non - perfect squares and $\pi$ are irrational.

Step 2: Analyze each option

• For $\frac{21}{19}$: Here, $p = 21$ and $q=19$ are both integers and $19

eq0$. So, $\frac{21}{19}$ can be written in the form $\frac{p}{q}$ with integer $p,q$ and $q
eq0$.

• For $\sqrt{2}$: 2 is not a perfect square. The decimal expansion of $\sqrt{2}\approx1.41421356\cdots$ is non - repeating and non - terminating, so it is irrational.
• For $\sqrt{55}$: 55 is not a perfect square. The decimal expansion of $\sqrt{55}\approx7.41619848\cdots$ is non - repeating and non - terminating, so it is irrational.
• For $\pi$: The decimal expansion of $\pi\approx3.14159265\cdots$ is non - repeating and non - terminating, so it is irrational.

Answer:

$\frac{21}{19}$