Use the product rule to simplify the expressions in Exercises 13–...

Question

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √125x^2

Accepted Answer

Welcome back. I'm so glad you're here. We are simplifying the expression, the square root of 81 X squared. And how did I know to write that square root bracket all the way over including the X squared because it's hard to tell from the way it's written up here. We got a couple of clues. We look at our answers and they've all just got a regular X instead of an X squared for their answers. So we know something's happening to that X squared. And also this part note that X is greater than or equal to zero. That's a domain restriction. And it tells us that something is happening to that X squared and we can't take the square root of a negative number. So that's why it has to be greater than or equal to zero. So we've got square root of 81 X squared. And we can break that down 81 that's going to be the same as nine times nine. X is the same as X times X. Now we can rewrite that again. Nine times nine is the same as nine squared X times X is the same as X squared. Yes. What we And the first one. But yeah. And so now we know that anything squared gets to come out when it is square rooted. And so nine squared? The square root of nine squared is going to be nine and the square root of X squared that comes right out of the bracket next to be X. And that can't be simplified anymore. So we look at our answer choices and that is answer choice B nine X. Well done. You've done, it will catch on the next one.