Introduction to Algebraic Operations with Radical Expressions

You can do more than just simplify radical expressions. You can multiply and divide them, too. Solving equations with radicals requires us to know how to perform mathematical operations on them like adding, subtracting, multiplying, and dividing.

When you learned how to solve linear equations, you probably learned about like terms first. We can only combine terms that are alike; otherwise, the terms will lose their meaning. When you learn how to perform algebraic operations on radical expressions in this section, you will use the concept of like terms in a new way.

You will also use the distributive property, rules for exponents, and methods for multiplying binomials to perform algebraic operations on radical expressions.

In particular, you will learn how to:

• Use properties of exponents to multiply radical expressions
• Use properties of exponents to divide radical expressions
• Identify radicals that can be added or subtracted
• Add radical expressions
• Subtract radical expressions
• Use the distributive property to multiply multiple terms radicals and then simplify
• Remove radicals from a single term denominator
• Rationalize denominators with multiple terms