This Math quiz is called 'Pre-Algebra - Simple Adding and Subtracting Radicals' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.
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In order to add radicals, there must be “like” terms in the problem. A problem with like terms would be 5x + 10x. Both terms contain the variable “x”. So the solution to 5x + 10x = 15x.
Let’s look at the next square root problem of 6√2 + 8√2. The like term here is √2. In addition to the √2 being like terms, so are the coefficient numbers “6” and “8” so you get to add those together, i.e., 6 + 8 = 14. The 14 is then placed before √2 and the solution is 14√2.
The same rule holds true for subtraction.
There must be “like” terms in the problem. Knowing this, if we look at the problem of: 9√p - 3√p the like term is √p and the coefficient numbers are 9 - 3 = 6. The 6 is then placed before the like term of √p giving us the solution of 6√p.
Now let’s look at another problem. 10√12 + 2√3. You cannot add these binomials because the terms are not like terms. However, you can simplify 10√12 to read 10√4 ● 3 and then the number 4 is the perfect square root of 2 so the 2 moves to the left of the √ symbol so that the problem now looks like: 10 ● 2√3. Next, 10 ● 2 = 20 giving you 20√3. Now we go back to the original problem and rewrite is as 20√3 + 2√3. We have √3 as our like term and then 20 + 2 = 22 which is placed before our like term giving us the solution of 22√3.
For each radical expression shown in the questions below, add or subtract to find the solution.