Adding and Subtracting Radical Expressions

Adding and subtracting radical expressions is similar to combining like terms: if two terms are multiplying the same radical expression, their coefficients can be summed. Some problems will not start with the same roots but the terms can be added after simplifying one or both radical expressions. Adding like radicals appears later in Algebra and frequently in Geometry.

Adding and subtracting radical expressions can be scary at first, but it's really just combining like terms.

Before we start, let's talk about one important definition. Two radical expressions are called "like radicals" if they have the same radicand. So this is a weird name. It's like radicals. It's not you don't say it like like radicals, you say it as like radicals. I don't know why we call them that. We're saying they're alike, if they have the same radicand. Remember, radicand's whatever that's under the square root.

Let's look at an example. Thinking about combining like terms, you guys can probably do this problem without ever learning how to do this process. What do you think the answer would be? 3 square roots of x plus 4 square roots of x equals, 7 square root of x. It's that easy. You combine the outside numbers as long as these are like radicals. Like radicals meaning it's the same thing under the square rooty.

In the second example though, we have different radicals, or unlike radicals. 3 square roots of x plus 4 square roots of y is it's just 3 square roots of x plus 4 square roots of y. Those guys can't be combined because they're unlike radicals. So you can combine them only if they have the same radicand, that's what you're looking for.

However, you guys know Math teachers don't like making anything easy. What you're going to see is sometimes you need to simplify the radicands to see if they're like radicals. They're not always going to look as easy like x and x. Sometimes you're going to have to do some simplifying by finding perfect square factors before you could recognise that those could be combined terms.