Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 3√xy - 8√xy

Verified step by step guidance

1. Identify the like terms: Both terms, \(3\sqrt{xy}\) and \(8\sqrt{xy}\), have the same radical part \(\sqrt{xy}\).
2. Since the radical parts are the same, you can combine the coefficients of the like terms.
3. Subtract the coefficients: \(3 - 8\).
4. Multiply the result by the common radical part \(\sqrt{xy}\).
5. Express the simplified form as a single term with the radical.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots, and are fundamental in algebra. In this context, the expression 3√xy and 8√xy represent cube roots of the product of variables x and y. Understanding how to manipulate these expressions is crucial for performing operations like addition or subtraction.

Combining Like Terms

Combining like terms is a key algebraic skill that involves simplifying expressions by adding or subtracting terms that have the same variable components. In the given expression, both terms contain the radical √xy, allowing them to be combined. This process simplifies the expression and makes it easier to work with.

Properties of Exponents and Radicals

The properties of exponents and radicals govern how to simplify and manipulate expressions involving powers and roots. For instance, the cube root can be expressed as an exponent of 1/3. Understanding these properties helps in rewriting and simplifying expressions, which is essential for solving algebraic problems effectively.