Question

2 which of these is a rational number? a $sqrt{254}$ b $\frac{sqrt{125}}{5}$ c $-\frac{sqrt{4}}{2}$ d $-sqrt{3}$

Explanation:

Step1: Recall the definition of rational numbers

A rational number can be written as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. Also, if a square - root of a non - negative integer is an integer, then the number is rational.

Step2: Analyze option A

$\sqrt{254}$ is not an integer because $15^2 = 225$ and $16^2=256$. So $\sqrt{254}$ is an irrational number.

Step3: Analyze option B

$\sqrt{125}=5\sqrt{5}$, then $\frac{\sqrt{125}}{5}=\frac{5\sqrt{5}}{5}=\sqrt{5}$. Since $\sqrt{5}$ is not an integer, $\frac{\sqrt{125}}{5}$ is an irrational number.

Step4: Analyze option C

$\sqrt{4} = 2$, so $-\frac{\sqrt{4}}{2}=-\frac{2}{2}=- 1$. Since $-1$ can be written as $\frac{-1}{1}$, it is a rational number.

Step5: Analyze option D

$-\sqrt{3}$ is an irrational number because $\sqrt{3}$ is not an integer.

Answer:

C. $-\frac{\sqrt{4}}{2}$