How to Add Square Roots

To add square roots, you first need to simplify each root as much as possible. Then, you can combine like terms by adding the coefficients (numbers in front of the square roots) together.

Here are the general steps to add square roots:

Step 1: Simplify each square root.

If possible, factor the number inside the square root and look for perfect squares to simplify.

For example, let's say you want to simplify:

√8 + √18

You can simplify the first square root as follows:

√8 = √(4 x 2) = 2√2

Similarly, you can simplify the second square root as follows:

√18 = √(9 x 2) = 3√2

Step 2: Combine like terms.

Now that you have simplified each square root, you can add them together by adding the coefficients (numbers in front of the square roots) together. In this example, you can combine the like terms as follows:

2√2 + 3√2 = (2+3)√2 = 5√2

So the sum of √8 and √18 is equal to 5√2.

In summary, to add square roots, simplify each square root and then combine like terms by adding the coefficients together.