In Exercises 39–60, simplify by factoring. Assume that all variab...

Question

In Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers.
__
√x⁵

Accepted Answer

Welcome back. I am so glad you're here. We're asked to simplify the following radical expression by factoring, assume that C is greater than zero. Our radical expression is the square root of C raised to the ninth power. Our answer choices are answer choice, ac answer choice BC raised to the fourth power square root. C answer choice C C cubed and answer choice DC cubed square. It C All right. The first step in simplifying our radicals is we want to look and see what our index is and when there is none written, then it is two. So what we want to do is get things in, we want factors in groups of two and then they are able to come outside of the radical. We have C raised to the ninth power. We can expand that and break that down into factors that do come in groups of two C raise to the ninth power is the same as C race to the fourth power multiplied by C race to the fourth power multiplied by C because we recall from previous lessons that when we're multiplying like bases, those are the CS, we get to add their exponents. So four plus four plus the unwritten one from the final C is nine, we can focus on this C race to the fourth power multiplied by C race to the fourth power because that is the same as C race to the fourth power squared. And there we have something squared that can come outside of our radical and that is still multiplied by C. So underneath our radical, we have the square root of instead of C to the ninth, we can write that as C to the fourth squared multiplied by C. And now anything that is squared can come out of our square rut, that's going to be this C race to the fourth power squared. And when it comes outside of the radical, it loses that squared. So it's just C race to the fourth multiplied by the square root of. And what's left inside the radical is just C, this is as simplified as this one gets and we look at our answer choices and it matches with answer choice B well done. We'll catch you on the next one.

In Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. __ √x⁵

Key Concepts

Factoring

Radicals

Exponents

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