Q(√2) refers to the set of all numbers that can be expressed as a combination of rational numbers and the square root of 2. This set includes numbers like 1, 2, and 3√2, which can be formed by adding, subtracting, multiplying, or dividing rational numbers with √2. In mathematical terms, Q(√2) is an example of a field extension, where the base field is the set of rational numbers, denoted as Q. This extension allows for the inclusion of irrational numbers, such as √2, expanding the types of numbers that can be used in calculations and algebraic expressions.