Overview:
Addition and subtraction of radicals is similar to addition and subtraction of polynomials. First, like terms must be identified. Some expressions may have to be simplified before they are in like terms. Then, they are added or subtracted as needed.
What Are Like Terms for Radicals?
Monomials such as 5ab and 3ab can be added to form 8ab, because they are like terms. Similarly, 3√3 and 2√3 can be added using the Distributive Property as (3+2)√3, or 5√3. Monomials such as 6√2 and 9√7 cannot be added as a single term, but remain separate. They form the polynomial expression 6√2 + 9√7.
Combine Like Terms:
Suppose the expression is something like 3√5 +2√3 +√5 +9√3. The Commutative Property can be used to put like terms in the same group. That way, it is easier to see that 3√5 and √5 can be added as 4√5 and 2√3 and 9√3 can be added as 11√3.
What About Variables?
Pay attention to variables when deciding if the terms are like terms. For example 3√a and 2√b are not like terms. They cannot be added as the same unit. However, 9√c and 12√c could be added as 21√c.
Can Any Terms Be Simplified?
Make sure before adding radicals that all terms are in the simplest form. Suppose the expression is √48 +6√27 – 5√12. The first term, √48, can be factored and simplified to √12√4, which can be further simplified to √4√3√4 or 4√3. The second term, 6√27, can be simplified to 6∙3√3, or 18√3. The third term, 5√12 can be simplified to 5∙2√3, or 10√3. The expression with everything in simplest terms is 4√3 + 18√3 – 10√3. Using the Distributive Property to combine like terms (4 + 18- 10)√3 equals 12√3. Unless everything were simplified, it would be impossible to know what the like terms were.
Interested in algebra tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Washington, DC visit: Tutoring in Washington, DC