A non-real, or imaginary, number is any number that, when multiplied by itself, produces a negative number. Mathematicians use the letter "i" to symbolize the square root of -1. An imaginary number is any real number multiplied by i. For example, 5i is imaginary; the square of 5i is -25.
No real negative number can have a negative square root, because even a negative number multiplied by itself produces a positive product. Real numbers are those numbers that represent a quantity along a number line, including all positive and negative numbers and zero. Irrational numbers, even though they cannot be expressed as a precise fraction or decimal, are considered real numbers because they do exist at some place on the number line, even if that place is not precisely defined.