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

검증된 단계별 안내

Recognize that the problem asks to identify the property illustrated by the expression \(5 + \sqrt{3}\), where all variables represent real numbers.

Recall that the set of real numbers is closed under addition, meaning that the sum of any two real numbers is also a real number.

Note that \(5\) is a real number and \(\sqrt{3}\) is also a real number because the square root of a positive real number is real.

Apply the closure property of addition: since both \(5\) and \(\sqrt{3}\) are real numbers, their sum \(5 + \sqrt{3}\) must also be a real number.

Conclude that the property illustrated here is the Closure Property of Addition for real numbers.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Real Numbers

Real numbers include all rational and irrational numbers that can be found on the number line. They encompass integers, fractions, and roots like √3, representing quantities with magnitude but no imaginary component.

Properties of Real Numbers

Real numbers are closed under addition, meaning the sum of any two real numbers is also a real number. This property ensures expressions like 5 + √3 remain within the set of real numbers.

Irrational Numbers

Irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions. √3 is an example, and when added to a rational number like 5, the result is still a real number.