What number sets does the square root of 9 fit into?

1 answer

The square root of 9 is 3. The number 3 fits into several number sets, including:

  1. Natural Numbers (ℕ): These are the positive integers starting from 1. Since 3 is a positive integer, it is a natural number.

  2. Whole Numbers (ℕ₀): Whole numbers include all natural numbers plus zero. Hence, 3 is also a whole number.

  3. Integers (ℤ): Integers include all whole numbers and their negative counterparts. Since 3 is a positive whole number, it is an integer.

  4. Rational Numbers (ℚ): Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. The number 3 can be expressed as \( \frac{3}{1} \), so it is a rational number.

  5. Real Numbers (ℝ): Real numbers include all rational and irrational numbers. Since 3 is a rational number, it is also a real number.

  6. Complex Numbers (ℂ): Complex numbers are numbers that have a real part and an imaginary part. The number 3 can be expressed as \( 3 + 0i \), which means it is also a complex number.

In summary, the number 3 fits into the sets of natural numbers, whole numbers, integers, rational numbers, real numbers, and complex numbers.