When it comes to adding and subtracting square roots, you can only do it if the radicands (the numbers inside), are the same. This boils the question down to:

Now we add the constants, the numbers on the outside, together.  The radicands stay the same:

Since each term in the expression has the same radical, the terms can be combined together by adding and subtracting their coefficients.

Thus to simplify this expression, combine the coefficients as follows.

Therefore, .

Thus, your answer is .

Step 1: Simplify the roots 1 by 1:





Step 2: Re-write the equation based on the simplified radicals.



Step 3: Add like terms:

. This is the final answer.

In order to add terms with radials, the radicands must be the same. In this case, both terms must contain .

The Power of a Product property of exponents states that . Since the taking the square root of a number is the same as raising it to the 1/2 power, then:

OR

In this problem:

The problem then becomes:

Adding and subtracting radicals cannot be done without having the same number under the same type of radical. These numbers first need to be simplified so that they have the same number under the radical before adding the coefficients. Look for perfect squares that divide into the number under the radical because those can be simplified.

Now take the square root of the perfect squares. Note that when the numbers come out of the square root they multiply with any coefficients outside that radical.

Since all the terms have the same radical, now their coefficients can be added

To add or subtract radicals, they must be the same root and have the same number under the radical before combining them. Look for perfect squares that divide into the number under the radicals because those can be simplified. However, in this problem all the numbers under the radicals are already perfect squares and can be simplified directly.

To add or subtract radicals, they must be the same root and have the same number under the radical before combining them. Look for perfect squares that divide into the number under the radicals because those can be simplified.

Take the square roots of each of the perfect squares in these radicals and bring it out of the radical. It will multiply to any coefficient in front of that radical

Finally, combine the coefficients of the same radicals

To add or subtract radicals, they must be the same root and have the same number under the radical before combining them. Look for perfect squares that divide into the number under the radicals because those can be simplified. In this problem, only the 12 divides by a perfect square

Take the square roots of each of the perfect squares in these radicals and bring it out of the radical. It will multiply to any coefficient in front of that radical

This is as far as the problem can be simplified.

To add or subtract radicals, they must be the same root and have the same number under the radical before combining them. Look for perfect squares that divide into the number under the radicals because those can be simplified. In this problem, 100 and 4 are already perfect squares and can be directly square rooted.

Take the square roots of each of the perfect squares in these radicals and bring it out of the radical. It will multiply to any coefficient in front of that radical

To add or subtract radicals, they must be the same root and have the same number under the radical before combining them. Look for perfect squares that divide into the number under the radicals because those can be simplified.

Take the square roots of each of the perfect squares in these radicals and bring it out of the radical. It will multiply to any coefficient in front of that radical