Question

1. name the subset(s) of the real numbers to which \\(\sqrt{25}\\) belongs.

Explanation:

Step1: Simplify the square root

First, calculate the value of $\sqrt{25}$. Since $5\times5 = 25$, we have $\sqrt{25}=5$.

Step2: Identify the subsets

Now, we analyze the number $5$. The subsets of real numbers that $5$ belongs to include:

• Natural Numbers (Counting Numbers): $5$ is a positive integer used for counting, so it belongs to the set of natural numbers ($\mathbb{N}$).
• Whole Numbers: Whole numbers include $0$ and all natural numbers, so $5$ is a whole number.
• Integers: Integers include all positive and negative whole numbers and $0$, so $5$ is an integer ($\mathbb{Z}$).
• Rational Numbers: A rational number is a number that can be expressed as a fraction $\frac{a}{b}$ where $a$ and $b$ are integers and $b

eq0$. Since $5=\frac{5}{1}$, it is a rational number ($\mathbb{Q}$).

• Real Numbers: All rational and irrational numbers are real numbers, so $5$ (and thus $\sqrt{25}$) is a real number ($\mathbb{R}$).

Answer:

The number $\sqrt{25} = 5$ belongs to the subsets: Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Real Numbers.