Add or subtract, as indicated. See Example 6.5√3 - √3

Verified step by step guidance

1. Identify the like terms in the expression: both terms contain \( \sqrt{3} \).
2. Factor out the common term \( \sqrt{3} \) from the expression.
3. Rewrite the expression as \( (5 - 1) \sqrt{3} \).
4. Simplify the expression inside the parentheses: \( 5 - 1 \).
5. Multiply the simplified result by \( \sqrt{3} \) to get the final expression.

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots. In this context, √3 represents the square root of 3. Understanding how to manipulate these expressions, including addition and subtraction, is crucial for simplifying them correctly.

Like Terms

Like terms are terms that contain the same variable raised to the same power or, in the case of radicals, the same root. For example, 5√3 and √3 are like terms because they both involve the square root of 3. Recognizing and combining like terms is essential for simplifying expressions.

Coefficient

A coefficient is a numerical factor in a term. In the expression 5√3, the coefficient is 5, indicating how many times the radical is counted. When performing operations with radical expressions, it is important to manage these coefficients correctly to arrive at the correct simplified form.