1. **State the problem:** Determine which category correctly describes the number $\sqrt{5}$. The options are: A. whole number B. Irrational C. rational D. integers 2. **Recall definitions:** - Whole numbers are non-negative integers: $0,1,2,3,\dots$ - Integers include all whole numbers and their negatives: $\dots,-2,-1,0,1,2,\dots$ - Rational numbers can be expressed as a fraction $\frac{a}{b}$ where $a,b$ are integers and $b\neq0$. - Irrational numbers cannot be expressed as a fraction of integers. 3. **Analyze $\sqrt{5}$:** $5$ is not a perfect square, so $\sqrt{5}$ is not a whole number or integer. 4. **Is $\sqrt{5}$ rational?** It cannot be expressed as a fraction of integers, so it is not rational. 5. **Conclusion:** $\sqrt{5}$ is an irrational number. **Final answer:** B. Irrational