 So let's take a look at the addition and subtraction of radicals when the radicands are different. So remember that we can add and subtract radicals if the radicands are the same. So five square roots of three and three more square roots of three will give us eight square roots of three. Or if you have eight square roots of two and you remove five of the square roots of two, then you'll have three square roots of two left over. But what if the radicands are different? So for example, let's say we want to simplify square root seventy-five plus square root of twenty-seven. So the radicands are not the same, so we can't add these two directly. We have to simplify them a little bit. And so we can try to simplify them. So remember that when simplifying a radical, a factor only matters if it's a perfect square. So we can try to remove the square factors. So square root of seventy-five, well I can factor seventy-five as square root twenty-five times three. But wait, the square root of a product of positive numbers is the same as the product of the square roots of the numbers. So we can rewrite this square root of twenty-five times three as square root twenty-five times the square root of three, and the square root of twenty-five is five. So this becomes five square roots of three. Similarly, square root of 27, I can factor this as square root of 9 times 3. The square root of a product is the product of the square roots, so this becomes square root of 9 times square root of 3. And square root of 9 is 3, so we'll replace it, and everything else stays the same. Square root of 27 is 3 square roots of 3. Equals means replaceable, so instead of square root 75, I'll write 5 square roots of 3. Instead of square root of 27, I'll write 3 square roots of 3. And now our radicans are the same. They're both square roots of 3, so I can add 5 and 3 square roots of 3, our total of 8 square roots of 3. How about a subtraction? Once again, the radicans are different, so we can't do anything immediately. But we can try to simplify. So square root of 150 is square root of 25 times 6, which we can simplify, to 5 square roots of 6. Square root of 96 is square root of 16 times 6, which is square root 16 times square root of 6, which we can simplify, to 4 square roots of 6. Equals means replaceable, so instead of square root 150, I'll write 5 root 6. Instead of square root of 96, I'll write 4 square roots of 6. And so I have 5 square roots of 6, and I'm going to remove 4 square roots of 6. So I'll have 5 minus 4 square roots of 6, otherwise known as 1 square root of 6.