Final answer:
C. Irrational and Real. The number √146 belongs to the sets of Irrational and Real numbers.
Step-by-step explanation:
The number √146 belongs to the set of Irrational numbers and the set of Real numbers.
To determine if √146 is an integer, rational, or irrational number, we need to find its value. Using a calculator, we find that √146 is approximately 12.0830459736. Since it is not a whole number or a fraction, it is irrational.
All irrational numbers are also real numbers, so √146 belongs to the sets of both irrational and real numbers.