In Exercises 47 - 49, add or subtract terms whenever possible. 7√5 + 13√5

Verified step by step guidance

1. Identify the like terms in the expression. In this case, both terms contain the square root of 5, making them like terms.
2. Since the terms are like terms, you can add or subtract the coefficients of these terms.
3. The expression is 7\sqrt{5} + 13\sqrt{5}.
4. Add the coefficients of the like terms: 7 + 13.
5. Combine the result with the common radical part, \sqrt{5}, to simplify the expression.

Key Concepts

Like Terms

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 5, making them like terms. This allows for the addition or subtraction of their coefficients, which simplifies the expression.

Coefficients

Coefficients are the numerical factors in front of variables or terms. In the expression 7√5 + 13√5, the coefficients are 7 and 13. When combining like terms, you add or subtract these coefficients while keeping the common term (√5) unchanged.

Simplifying Expressions

Simplifying expressions involves combining like terms and reducing expressions to their simplest form. In this case, adding the coefficients of the like terms results in a more concise expression, demonstrating the process of simplification in algebra.