How Do You Add Radicals with Like Radicands?

The symbol above 15 is a square root sign
Adding radicals is just like adding with variables
The value underneath the radicals must be the same in order to add the radicals together
The numbers in front of 'x' are called coefficients
Use the Distributive Property to factor 'x' out of the problem
Then just add the coefficients to simplify

1. We can't just add together what's underneath the radical
2. Instead, we treat the radicals sort of like variables when we add
1. We're going to pretend that our √(15)'s are variables instead
1. It's easier to add radicals together if you treat them like variables
2. Let's choose the variable 'x' to represent the square root of 15
3. This lets us easily see like terms that we can add together
4. We can take 'x' and use the Distributive Property to factor it out, so we get (6+2+3)x
1. Adding radicals is just like adding variables
2. The radicals need to be EXACTLY the same, otherwise we can't add them
1. Adding radicals is just like adding variables
2. We want to add like terms together
3. Radicals with the same value under the square root sign are like terms
1. Just like we did with 'x', we can use the Distributive Property to factor out the square root of 15
2. So we'll have (6+2+3)•√(15)
1. Simplify by adding the coefficients together
2. Our coefficients are 6, 2, and 3
1. Simplify by adding the coefficients together
2. Our coefficients are 6, 2, and 3
3. 6 + 2 + 3 = 11
1. 15 doesn't have any perfect square factors, so our expression is in simplest form

Add these radicals: 6√15 + 2√15 +3√15