Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) √24

검증된 단계별 안내

First, recognize that the number given is \( \sqrt{24} \). Since 24 is a positive real number, its square root is also a real number.

Simplify \( \sqrt{24} \) by factoring 24 into its prime factors: \( 24 = 4 \times 6 \). Then, \( \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} \).

Calculate \( \sqrt{4} \), which is 2, so \( \sqrt{24} = 2\sqrt{6} \). This is a real number because it is a product of real numbers.

Since \( \sqrt{24} \) is a real number and does not involve the imaginary unit \( i \), it is not complex in the sense of having an imaginary part, nor is it pure imaginary or nonreal complex.

Therefore, \( \sqrt{24} \) is classified as a real number (and also a complex number because all real numbers are a subset of complex numbers), but it is not pure imaginary or nonreal complex.

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주요 개념

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Real Numbers

Real numbers include all rational and irrational numbers that can be found on the number line. They encompass integers, fractions, and roots of positive numbers, such as √24, which is a positive real number because it represents a non-negative value.

Complex Numbers

Complex numbers are numbers in the form a + bi, where a and b are real numbers and i is the imaginary unit with i² = -1. Every real number is also a complex number with b = 0, so √24 can be considered a complex number with zero imaginary part.

Pure Imaginary and Nonreal Complex Numbers

Pure imaginary numbers have the form 0 + bi where b ≠ 0, meaning they lie entirely on the imaginary axis. Nonreal complex numbers have a nonzero imaginary part. Since √24 has no imaginary part, it is neither pure imaginary nor nonreal complex.