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In mathematics, 'like terms' are terms that have precisely the same variable part — this means they have the same variables raised to the same power. For example, the given terms in our practice problem, \(2 \sqrt{x}\) and \(9 \sqrt{x}\), both contain the square root of \(x\).
This makes them like terms because the variable part \(\sqrt{x}\) is the same. Without like terms, combining terms in expressions can become very tricky.

When simplifying expressions, identifying like terms is a crucial first step. It helps to group terms that can be combined, making the expressions much simpler and easier to manage.
Remember: Only terms with exactly the same variable parts are like terms. Constants (numbers without variables) are also considered like terms with each other because they essentially share the same 'variable' part of being constant.

Coefficients are the numerical parts of a term that are multiplied by the variable part. For instance, in the term \(2 \sqrt{x}\), the coefficient is 2. In \(9 \sqrt{x}\), the coefficient is 9.
Understanding coefficients is key when working with like terms because it tells us how many of these terms we have.

In the practice problem, the term \(2 \sqrt{x}\) tells us we have 2 units of \(\sqrt{x}\), while the term \(9 \sqrt{x}\) tells us we have 9 units of \(\sqrt{x}\).
This understanding of coefficients helps in combining terms through arithmetic operations like addition, subtraction, etc. Remember, you only ever add or subtract coefficients of like terms and keep the variable part unchanged.

Combining like terms is the process of simplifying an expression by adding or subtracting the coefficients of like terms. This makes the expression shorter and easier to understand.
When combining like terms, just add or subtract the coefficients and keep the variable part the same.

For example, in the expression \(2 \sqrt{x} + 9 \sqrt{x}\), we recognize both terms as like terms. We then combine them by adding their coefficients: \(2 + 9 = 11\).
Thus, \(2 \sqrt{x} + 9 \sqrt{x} = 11 \sqrt{x}\), where the coefficient is now the sum of the original coefficients while the variable part \(\sqrt{x}\) remains unchanged.

This method is essential for simplifying algebraic expressions, solving equations, and making math problems easier to handle. Always ensure you correctly identify like terms and their coefficients before combining them to avoid errors.