Simple Steps for Adding
Square Roots

On this page you'll find...

You'll be happy to hear that adding square roots follows many of the rules as other algebraic terms.

In fact, the most important rule is...

When Adding Square Roots You Can Only Combine "Like Terms"

Remember "like terms"?  Yes, we can only add or subtract square roots (or any radical) if they are like terms.

So, let's look at a few examples.

What are Square Roots that are Like Terms?

When working with square roots, like terms will have the exact same radicand.

(Remember the radicand is the expression inside the radical)

When adding square roots, like terms must have the same radicand.
Examples of like terms and not like terms for square roots

So, if your square roots are like terms, then you can add them together!  Let's take a look at a few examples.

Example 1: Adding Square Roots

Identify the like terms and then add the square roots.

Notice how in this example, we can add the two square roots that have a radicand of 5.  The square root of three is not a like term, so it can not be combined.

Example 2: Simplify Before Adding Square Roots

Before adding square roots, always check to see if any can be simplified.  Sometimes the square roots can even be simplified to whole numbers!

Add the square root of nine, plus the square root of 25.

Since the square root of 9 equals 3 and the square root of 25 equals 5, this problem can be simplified to a whole number.

Example 3:  More Simplifying Before Adding

Be careful not to automatically just assume that since your radicands are not exactly the same that you don't have like terms.

Remember that you must simplify first, then determine if you have like terms. 

Notice in this next example that 2 times the square root of 8 can be simplified to 4 square roots of 2 and then this creates like terms that can be added together.

Add two square roots of eight and six square roots of two to get an answer of ten square roots of two.

The most important thing to remember when adding square roots is that you can only add like terms.

It's also important to remember that you must always simplify square roots first and then determine if you have like terms.

I hope that these examples help you as you learn how to add square roots.

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