Learning Objectives:

__Adding and Subtracting Radicals __

There are two keys to combining **radicals** by addition or subtraction: look at the index, and look at the **radicand**. Two or more **radical **expressions are called **like radicals** if they have the same index and the same **radicand**. **Radicals** that are **like radicals** can be added or subtracted by adding or subtracting the coefficients, so this works very similar to how we combine like terms. But now we're dealing with **like** **radicals**, so here are guidelines that we'll follow:

1) We’ll simplify each **radical**.

2) We'll identify the **like radicals**.

3) We'll add or subtract the **like radicals** by adding or subtracting the coefficients. We can't add or subtract two **radicals** unless they have the exact same number inside the root. When inside the roots are the same, simply add or subtract the outside numbers together and keep the root the same and simplify the **radical**. Sometimes when we don't see **like radicals** we may need to simplify the radicals so that we can identify similar ones.

**Hook Questions**:

1*. What is a like radical? *

*2. How do you add square roots with different radicals? *

*3. When can you add and subtract radicals?*

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