Add or subtract terms whenever possible. $4\(\sqrt\)[5]{2} + 3\(\sqrt\)[5]{2}$

Verified step by step guidance

1. Identify the like terms in the expression. Both terms have the fifth root of 2, which can be written as \(4 \sqrt[5]{2}\) and \(3 \sqrt[5]{2}\).
2. Since the radical parts are the same (\(\sqrt[5]{2}\)), you can combine the coefficients (the numbers in front of the radicals).
3. Add the coefficients: \$4 + 3 = 7$.
4. Write the combined expression as the sum of the new coefficient and the common radical: \(7 \sqrt[5]{2}\).
5. This is the simplified form of the expression after combining like terms.

Key Concepts

Like Terms

Like terms are terms that have the same variable parts raised to the same powers. In expressions involving radicals, terms with the same radicand and root index can be combined by adding or subtracting their coefficients.

Radical Expressions

A radical expression involves roots, such as square roots or fifth roots. Understanding how to interpret and manipulate radicals, including recognizing when two radicals are like terms, is essential for simplifying expressions.

Simplifying Expressions

Simplifying expressions involves combining like terms and reducing expressions to their simplest form. This includes adding or subtracting coefficients of like radical terms to write the expression more concisely.