Adding and Subtracting Radicals

Adding and Subtracting Radicals

Learning Objectives:

Understand to Add and Subtract Radicals.

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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