Add or subtract, as indicated. See Example 6.√6 + √7

Verified step by step guidance

1. Identify the terms involved: \( \sqrt{6} \) and \( \sqrt{7} \).
2. Recognize that these are both square roots of different numbers.
3. Understand that \( \sqrt{6} \) and \( \sqrt{7} \) are not like terms, meaning they cannot be combined into a single term.
4. Since they are not like terms, the expression \( \sqrt{6} + \sqrt{7} \) is already in its simplest form.
5. Conclude that the expression remains \( \sqrt{6} + \sqrt{7} \) as the final simplified form.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. In this case, √6 and √7 are square roots of the numbers 6 and 7, respectively. Understanding how to manipulate these expressions is crucial for performing operations like addition or subtraction.

Like Terms

In algebra, like terms are terms that have the same variable raised to the same power. When adding or subtracting radical expressions, it is essential to identify like terms. Since √6 and √7 are not like terms, they cannot be combined directly, which is a key aspect of this problem.

Simplifying Radical Expressions

Simplifying radical expressions involves reducing them to their simplest form, which can include factoring out perfect squares. While √6 and √7 cannot be simplified further, understanding this process is important for more complex problems involving radicals, as it can affect how expressions are combined.