WHY IS IT IMPORTANT TO SIMPLIFY RADICAL EXPRESSIONS BEFORE ADDING OR SUBTRACTING? HOW IS ADDING RADICAL EXPRESSIONS SIMILIAR TO ADDING POLYNOMIAL EXPRESSIONS?
It is important to simplify radical expressions before adding or subtracting because it allows us to work with simplified and organized expression, making calculations much easier. Simplifying radical expressions involves finding perfect square factors and simplifying any radical terms, which can help us identify any like terms and combine them accordingly.
Adding radical expressions is similar to adding polynomial expressions in the sense that we focus on combining like terms. Just like in polynomial addition, we look for terms with similar characteristics (same radicands and same variables and exponent in the case of polynomials) and then combine them by adding their coefficients. By simplifying radical expressions beforehand, we make sure that we have identified all the like terms and combined them correctly, which leads to an accurate and simplified result.
To simplify radical expressions before adding or subtracting them, follow these steps:
1. Identify any perfect square factors inside the radicals. If any number or variable inside the radical can be written as the square of a whole number or a variable, simplify it.
2. Simplify any radical terms by combining like terms if possible. Identify radical terms with the same radicands and combine them.
3. Once all the radical expressions are simplified, check if there are any like terms that can be added or subtracted.
4. Finally, combine the coefficients of the like terms to obtain the simplified sum or difference of the radical expressions.
By following these steps, we ensure that the radical expressions are simplified and organized, making it easier to perform addition or subtraction accurately.