Adding and Subtracting Radical Expressions - Concept
Simplifying rational expressions combines everything learned about factoring common factors and polynomials. When simplifying rational functions, factor the numerator and denominator into terms multiplying each other and look for equivalents of one (something divided by itself). Include parenthesis around any expression with a "+" or "-" and if all terms cancel in the numerator, there is still a one there.
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.