Yes, √4 is a real number.
The square root of 4, denoted as √4, is equal to 2. Numbers can be classified as either real or imaginary. Real numbers include all rational and irrational numbers and can be represented on a number line, while imaginary numbers involve the square root of negative one (denoted as 'i'). A number is considered real if its imaginary component is zero, meaning it can be written in the form a + 0i where 'a' is the real part of the number.
According to the reference: "If b=0, then the number is real. If b is not equal to 0, then it is imaginary. Since root 4 is 2 (or 2+0i), root 4 is a real number." This clearly states that because √4 equals 2, and can be expressed as 2 + 0i, it falls under the definition of a real number.
Here's a breakdown:
- Real Numbers: Numbers that can be plotted on a number line. This includes integers, rational numbers, and irrational numbers. Examples include -3, 0, 2, 1/2, and √2.
- Imaginary Numbers: Numbers that have a non-zero imaginary component represented by 'i', where i = √-1. These are typically expressed as bi, where 'b' is a real number. Examples include 2i, -5i, and i√3.
- Complex Numbers: Numbers that combine a real and imaginary part, expressed as a + bi, where 'a' and 'b' are real numbers. Real numbers are a subset of complex numbers where 'b' equals zero.
| Number | Real Part | Imaginary Part | Real? |
|---|---|---|---|
| 2 | 2 | 0 | Yes |
| 2 + 3i | 2 | 3 | No |
| 0 | 0 | 0 | Yes |
| i | 0 | 1 | No |
| √4 | 2 | 0 | Yes |
Therefore, as √4 = 2, and 2 can be represented as 2 + 0i, it is definitively a real number because the imaginary component is 0.
