Identify the property illustrated in each statement. Assume all variables represent real numbers.5 + √3 is a real number.

Verified step by step guidance

1. Identify the type of numbers involved in the expression: 5 is a real number and \( \sqrt{3} \) is also a real number.
2. Recognize that the operation involved is addition, which is a basic arithmetic operation.
3. Recall the closure property of real numbers, which states that the sum of any two real numbers is also a real number.
4. Apply the closure property to the expression: Since both 5 and \( \sqrt{3} \) are real numbers, their sum, 5 + \( \sqrt{3} \), is also a real number.
5. Conclude that the property illustrated by the statement '5 + \sqrt{3} is a real number' is the closure property of addition for real numbers.

Key Concepts

Real Numbers

Real numbers include all the numbers that can be found on the number line, encompassing both rational numbers (like integers and fractions) and irrational numbers (like √3). They are used to represent quantities and can be positive, negative, or zero. Understanding that 5 and √3 are both real numbers is essential for analyzing expressions involving them.

Properties of Real Numbers

The properties of real numbers include various rules that govern their operations, such as the commutative, associative, and distributive properties. These properties help in simplifying expressions and solving equations. Recognizing that the sum of two real numbers (5 and √3) is also a real number illustrates the closure property of real numbers.

Closure Property

The closure property states that when you perform an operation (like addition or multiplication) on two numbers from a set, the result will also belong to that set. In this case, since both 5 and √3 are real numbers, their sum (5 + √3) is also a real number, demonstrating the closure property of real numbers under addition.