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.
It costs only $12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us
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.
As we do not have like terms we must simplify as follows:
45√72 = 45√36 ● 2
As 36 is a perfect square in that 6 ● 6 = 36, the 6 goes before or to the left of the √ symbol giving you 6 ● 45√2
6 ● 45 = 270 and then add on the √2 giving you 270√2. Now the problem can be rewritten as: 270√2 - 221√2 = 49√2
Solution: 49√2
Answer (c) is the correct solution