Perform the indicated operations. Assume all variables represent positive real numbers. 5√6 + 2√10

Verified step by step guidance

1. Identify the terms in the expression: \(5\sqrt{6}\) and \(2\sqrt{10}\).
2. Recognize that these terms are not like terms because they have different radicands (6 and 10).
3. Since the terms are not like terms, they cannot be combined through addition.
4. The expression is already in its simplest form as \(5\sqrt{6} + 2\sqrt{10}\).
5. If needed, you can approximate the values of \(\sqrt{6}\) and \(\sqrt{10}\) to get a numerical approximation, but the exact expression remains as is.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. In the expression 5√6 + 2√10, the terms 5√6 and 2√10 are both radical expressions. Understanding how to manipulate these expressions is crucial for performing operations like addition or simplification.

Like Terms

Like terms are terms that contain the same variable raised to the same power or, in the case of radicals, have the same radicand (the number under the root). In the expression given, 5√6 and 2√10 are not like terms because √6 and √10 are different. Recognizing like terms is essential for combining them through addition or subtraction.

Simplifying Radicals

Simplifying radicals involves reducing the expression to its simplest form, which may include factoring out perfect squares from under the radical. While the expression 5√6 + 2√10 cannot be simplified further due to the different radicands, understanding how to simplify radicals is important for more complex operations and expressions.