In Exercises 75–82, add or subtract terms whenever possible. 4⁵√2+3⁵√2

Verified step by step guidance

1. Identify the like terms in the expression. Here, both terms have the same radical part, \( \sqrt[5]{2} \).
2. Since the terms are like terms, you can combine them by adding their coefficients.
3. The coefficients of the terms are 4 and 3.
4. Add the coefficients: 4 + 3.
5. Combine the result with the common radical part, \( \sqrt[5]{2} \), to form the simplified expression.

Key Concepts

Radicals

Radicals are expressions that involve roots, such as square roots or cube roots. In this case, the expression includes fifth roots, denoted as ⁵√. Understanding how to simplify and manipulate radical expressions is essential for combining like terms effectively.

Like Terms

Like terms are terms that have the same variable raised to the same power, or in the case of radicals, the same root. For example, 4⁵√2 and 3⁵√2 are like terms because they both contain the fifth root of 2. Recognizing and combining like terms is crucial for simplifying algebraic expressions.

Combining Terms

Combining terms involves adding or subtracting coefficients of like terms to simplify an expression. In the given problem, you would add the coefficients of the like terms 4 and 3, resulting in 7⁵√2. This process is fundamental in algebra for simplifying expressions and solving equations.