Add or subtract, as indicated. See Example 6.2√3 + 5√3

Verified step by step guidance

1. Identify the terms that are being added: \(2\sqrt{3}\) and \(5\sqrt{3}\).
2. Notice that both terms have the same radical part, \(\sqrt{3}\), which means they are like terms.
3. Since they are like terms, you can add the coefficients of the radicals together.
4. Add the coefficients: \(2 + 5\).
5. Multiply the sum of the coefficients by the common radical: \((2 + 5)\sqrt{3}\).

Key Concepts

Like Terms

In algebra, like terms are terms that have the same variable raised to the same power. In the context of this question, both terms involve the square root of 3, making them like terms. This allows for straightforward addition or subtraction of their coefficients, which is essential for simplifying expressions.

Coefficients

Coefficients are the numerical factors in front of variables or terms in an expression. In the expression 2√3 and 5√3, the coefficients are 2 and 5, respectively. When adding or subtracting like terms, you combine these coefficients while keeping the common radical part unchanged, which is a fundamental operation in simplifying expressions.

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, etc. In this question, √3 is a radical expression. Understanding how to manipulate radical expressions, including combining them when they are like terms, is crucial for solving problems that involve addition or subtraction of such terms.