When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated. Even though it's not the same, double check you can simplify the radicand. Look for perfect squares.  

Since 

 and  are perfect squares, we can rewrite like this:

Lets add everything up. 

We can only add or subtract radicals if they have the same radicand (part underneath the radical.

Combine the radicals with the radicand 3:

   the three in front of the radical came from the 1 in the original problem. It is not written but understood to be there similar to how the whole number 5 is understood to be over 1: 5/1=5

Now take the perfect square and multiply by the constant outside the radical:

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.

When adding or subtracting radicals, the radicand value must be equal. Since  and  are not the same, we leave the answer as it is. Answer is .

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 .

Since the radicand are the same, we can subtract with the coefficients. Since  is greater than  and is negative, our answer is negative. We treat as a subtraction problem. Answer is .

Although the radicands are different, we can simplify them to see if they can have the same radicands. We need to find perrfect squares.

 Indeed we have the same radicands, so we can add them easily with the coefficients.

Answer is .

Although the radicands are different, we can simplify them to see if they can have the same radicands. We need to find perrfect squares.

 Indeed we have the same radicands, so we can subract them easily with the coefficients.

Answer is .

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".

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