Use the product rule to rewrite the term inside the radical as a product, then simplify. − 72 x 2 -\sqrt{72x^2}

Before we get into this problem, I want to give a disclaimer that this was a tricky one. So if you didn't get this on your first try, that is totally Okay. This is a harder problem. So you can think of this as sort of an extra challenge problem and not one that you should be expected to solve on your first go around at the product rule. But if you did get this on the first try, amazing job. Otherwise, let's walk through it together, and we'll see exactly how to work this out. We're looking here to use the product rule to rewrite the term inside the radical as a product and then simplify. We're given here a negative square root of 72 x squared. So I have a number, but I also have a variable term underneath my radical as well. So I want to first rewrite this as a negative square root of 72 times x squared. So I already have a product there, but I can further break down this 72 in order to get this radical to simplify as much as possible. So that's what we wanna do here. Remember, previously, we rewrote a number as a product containing a perfect square. And that's what we wanna do for 72 here. So we wanna look at the factors of 72 and find which one has the largest perfect square factor. So 72, I'm gonna write out all my factors here. One times 72, two times 36, three times 24, four times 18. I have six times 12, and finally, I have eight times nine. Now if you recognize early on that this is gonna be the one with the largest perfect square, you can go ahead and stop there, but it's always a good idea just to double check. So we have two times 36. 36 is our largest perfect square factor. So that's what we wanna break down 72 into, the product of two and thirty six. So rewriting this as a negative square root of two times 36 times x squared. We can't forget that that variable term is there. Now because I have three things being multiplied underneath this one radical, I can actually break this apart into the multiplication of three separate radicals using the product rule. So rewriting this as negative square root of two times square root of 36 times square root of x squared. Now we can do some simplification. Because the square root of 36 is six, and this square root will cancel that square on my x. So this becomes a negative root two times six times x. Now when working with constants and square roots, we typically wanna put our constant out in front of our square root. So I would actually wanna rewrite this as negative six root two times x. And this is my fully simplified radical expression. Now we're gonna see how to work with these more advanced and challenging square roots in more detail coming up in future lessons. But for now, you can see a taste of exactly the kinds of radicals we're going to be dealing with as we continue on. Now that you got through this problem, great job. We're going to continue on, and I'll see you in the next video.

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Use the product rule to rewrite the term inside the radical as a product, then simplify.−72x2-\(\sqrt{72x^2}\)

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Use the product rule to rewrite the term inside the radical as a product, then simplify.
$- \sqrt{72 x^{2}}$