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. √27

Accepted Answer

Welcome back. I'm so glad you're here. We are simplifying the expression, the square root of 81 divided by the square root of 16. Now we can break this down. The square root of 81 is the same as the square root of nine times nine. The square root of 16 is the same as the square of four times four. And those are equivalent to the square root of nine squared, divided by the squared of four squared. And anything that's squared gets to come out of the square root. So woo! The nine gets to come out and eliminates the square root on top and the four gets to come out and eliminates the square root on the denominator. Great. We've got 9/4 and that can't be simplified any further than nine. Can only be divided by three. Four can only be divided by two. They have no common factors. So we look at our answer choices and a is correct. nine divided by four. That's it. You've done it. We'll catch you on the next one.