Question

which of the following is a rational number? √6, √94, √96, 57

Explanation:

Step1: Recall Rational Number Definition

A rational number is a number that can be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q
eq0$. Integers are rational (e.g., $57=\frac{57}{1}$). Square roots of non - perfect squares are irrational.

Step2: Analyze $\sqrt{6}$

6 is not a perfect square (since $2^2 = 4$ and $3^2=9$), so $\sqrt{6}$ is irrational.

Step3: Analyze $\sqrt{94}$

94 is not a perfect square (since $9^2 = 81$ and $10^2 = 100$), so $\sqrt{94}$ is irrational.

Step4: Analyze $\sqrt{96}$

96 is not a perfect square (since $9^2 = 81$ and $10^2 = 100$), so $\sqrt{96}$ is irrational.

Step5: Analyze 57

57 is an integer, and integers are rational numbers as $57=\frac{57}{1}$ (where $p = 57$ and $q = 1$ are integers and $q
eq0$).

Answer:

57