Simplify 12 square root five plus three square root five.
In order to add square roots, the number inside of the root must be exactly the same as the other one inside of the square root. And we have that. They’re both square root five. So we will keep that square root five and we will add the numbers in front of them.
So we will have 12 plus three and then square root five. And 12 plus three is equal to 15. This means that our answer will be 15 square root five.
Sometimes, it’s useful to think when adding and subtracting square roots is to treat them like variables. Imagine this to be 12𝑥 plus three 𝑥. So the square root fives represent like variables. They’re both 𝑥s. They’re both square root fives. So 12𝑥 plus three 𝑥 is 15𝑥. We keep the 𝑥 just like we keep the square root five as long as they’re the same.
So if one of the square root fives haven’t had been different, we wouldn’t have been able to combine them. Just like if this had been a three 𝑦, we wouldn’t be able to combine 12𝑥 and three 𝑦. We would simply have to leave them apart.
So once again, our final answer will be 15 square root five.