-√64 is categorized as a real number, a rational number, and an integer.
1. Real Numbers: Real numbers include all rational and irrational numbers. -√64 is a real number because it can be expressed as -8, which is a rational number. Rational numbers can be written as a fraction or a terminating or repeating decimal.
2. Rational Numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Since -√64 can be written as -8, which is a fraction -8/1, it is a rational number.
3. Integer: An integer is a whole number that can be either positive, negative, or zero. -√64 is an integer because it equals -8, which is a whole number and also negative.