 Remember that in a radical expression like principal square root of x, we require x to be non-negative. This means that all our rules for working with the square roots of real numbers apply to the square roots of variable expressions. And in particular, if we're adding or subtracting two expressions with the same radicand, we can add or subtract the coefficients. So, let's say I want to add 5 square root of x plus 7 square root of x. Since the radicands are the same, we can add the coefficients, and the radicand stays the same. Likewise, we can subtract 8 square root of x minus square root of x. Since the radicals are the same, we can subtract the coefficients. And here it's useful to remember if no coefficient is explicitly written, you may assume there is an implied 1. So this square root of x, well, that's really 1 square root of x. And so we'll subtract our coefficients 8 minus 1, and we'll keep that square root of x. How about 8 square root of 8x plus 2 square root of 50x? Since the radical expressions are the same, we could add the coefficients. What's that? Oh, wait, they're not the same. Since the radical expressions are not the same, we can't combine them. Or can we? We might be able to simplify the expression. So remember the square root of n squared times p is n times the square root of p. And so this means we might be able to simplify these expressions. And it's useful to remember when simplifying radicals, we want to look for perfect square factors. So we might be able to simplify the radicals. Let's take a look at that first expression, 8 square root of 8x. Now we'll look at that radicand and we'll look for a perfect square factor. And we know that 8x is 4 times 2x. And since I have a square root of a product, I can rewrite that as the product of the square roots. That's square root of 4 times square root of 2x. Square root of 4 is, and everything else is still there. And I do know how to multiply 8 times 2. And so when I simplify, I get 16 square root of 2x. How about this 2 square root of 50x? Well again, we'll try to look for perfect square factors in the radicand. And that gives us 25 times 2x. The square root of a product is the product of the square roots. I know what square root of 25 is. And simplify. And after simplification, both radicals are the same, so we can add the coefficients. And we can extend this process to however many of radicals we have. And so here, since all of our radicals are different, we can try to simplify them. So for 5 square root of 18x, let's try to find a perfect square factor of 18x. That would be 9 times 2x. The square root of a product is the product of the square roots. I know what the square root of 9 is. And I can multiply 5 times 3. 2 square root of 12x can be simplified as 7 square root of 75x becomes. And we do have two different radicals here, square root of 2x, square root of 3x, but we can combine the coefficients of the like radicals. So that would be these two, so we'll subtract the coefficients. And since the remaining radicals are not the same, we can't combine them in any meaningful way. So we'll have to leave them.