Algebra II : Adding and Subtracting Radicals
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Example Questions
Example Question #21 : Adding And Subtracting Radicals
Simplify this radical:
We can only add or subtract radicals if they have the same radicand (part underneath the radical.
Combine the radicals with the radicand 3:
Now take the perfect square and multiply by the constant outside the radical:
Example Question #22 : Adding And Subtracting Radicals
Simplify, if possible:
The radicals given are not in like-terms. To simplify, take the common factors for each of the radicals and separate the radicals. A radical times itself will eliminate the square root sign.
Now that each radical is in its like term, we can now combine like-terms.
Example Question #23 : Adding And Subtracting Radicals
When adding or subtracting radicals, the radicand value must be equal. Since 
Example Question #21 : Adding And Subtracting Radicals
Since they share the same radicand, we can add them easily. We just add the coefficients in front of the radical. So our answer is 
Example Question #25 : Adding And Subtracting Radicals
Since the radicand are the same, we can subtract with the coefficients. Since 
Example Question #26 : Adding And Subtracting Radicals
Although the radicands are different, we can simplify them to see if they can have the same radicands. We need to find perrfect squares.
Answer is 
Example Question #21 : Adding And Subtracting Radicals
Although the radicands are different, we can simplify them to see if they can have the same radicands. We need to find perrfect squares.
Answer is 
Example Question #21 : Adding And Subtracting Radicals
The answer is not present
We can only combine radicals that are similar or that have the same radicand (number under the square root).
Combine like radicals:
We cannot add further.
Note that when adding radicals there is a 1 understood to be in front of the radical similar to how a whole number is understood to be "over 1".
Example Question #29 : Adding And Subtracting Radicals
Simplify the following expression:
To simplify the expression, we must remember that only terms with the same radical can be added or subtracted, and when we add or subtract the terms, we are only doing so to the coefficients. (Think of the radicals as a variable. When we add two terms, we add coefficients of the same variable together but we never change the variable.)
Keeping this in mind, we get
Example Question #30 : Adding And Subtracting Radicals
Add:
First you must find the factors of each number which will give you one perfect square and a non perfect square as follows:
And remembering a property of the square root:
Making the problem now:
Take the square root of the known perfect squares:
Combine like terms to give the answer:
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