which number is not a rational number?\n-5\\frac{4}{11}\n\\sqrt{31}\n7.608\n18.4\\overline{6}

Answer:

B. $\sqrt{31}$

Explanation:

Step1: Recall rational number definition

A rational number can be written as $\frac{p}{q}$ where $p,q$ are integers and $q\neq0$.

Step2: Analyze $- 5\frac{4}{11}$

$-5\frac{4}{11}=-\frac{5\times11 + 4}{11}=-\frac{59}{11}$, so it's rational.

Step3: Analyze $7.608$

$7.608=\frac{7608}{1000}$, so it's rational.

Step4: Analyze $18.4\overline{6}$

Let $x = 18.4\overline{6}$. Then $10x=184.6\overline{6}$ and $100x = 1846.6\overline{6}$. Subtracting $10x$ from $100x$ gives $90x=1846.6\overline{6}-184.6\overline{6}=1662$, so $x=\frac{1662}{90}$, it's rational.

Step5: Analyze $\sqrt{31}$

$\sqrt{31}$ cannot be written as a fraction of two integers. It is an irrational number.