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Adding and Subtracting Radical Expressions  Concept
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
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.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Sample Problems (9)
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Adding and Subtracting Radical Expressions
Problem 1 10,141 viewsSimplify:
8√3 − 5√3 + 10√3 
Adding and Subtracting Radical Expressions
Problem 2 8,763 viewsSimplify:
4√5 − 3√45 + 10√80 
Adding and Subtracting Radical Expressions
Problem 3 7,190 viewsSimplify:
√125x + 4√20x − 3√45x 
Adding and Subtracting Radical Expressions
Problem 4 6,361 viewsSimplify:
3√x + y√x + 2√y²x 
Adding and Subtracting Radical Expressions
Problem 5 1,001 views 
Adding and Subtracting Radical Expressions
Problem 6 1,253 views 
Adding and Subtracting Radical Expressions
Problem 7 842 views 
Adding and Subtracting Radical Expressions
Problem 8 661 views 
Adding and Subtracting Radical Expressions
Problem 9 684 views
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