# Irrational Sums

## Worksheet Description

The worksheet is an exercise in adding numbers that involve both rational and irrational elements. Problems include adding mixed numbers with both integer and radical components, which can test a student’s ability to combine like terms and work with square roots. Some of the additions involve simple numerical fractions, while others are more complex, requiring the addition of radicals which may result in either a rational or an irrational sum. The variety of problems helps students practice and apply addition rules in different contexts.

The purpose of this worksheet is to develop students’ skills in the addition of mixed numbers, particularly those involving square roots, which are often found in algebra and pre-calculus courses. It teaches students how to identify and combine like terms, how to simplify radical expressions, and how to manage the addition of both rational and irrational numbers. The exercise reinforces the concept that addition can be performed between like terms and that the sum of rational numbers is rational, while the sum involving an irrational number may be irrational. This practice is crucial for students to understand how different types of numbers interact in addition, setting the foundation for more advanced algebraic operations.