Simplify the radical expressions in Exercises 67–74, if possible....

Question

Simplify the radical expressions in Exercises 67–74, if possible. ³√150

Accepted Answer

Welcome back. I'm so glad you're here. We've got this radical, the cubed root of 990 and we are to simplify it if possible. Well whenever we want to simplify a radical we want to look and see what number is here that tells us how many of something you need to bring it out of the radical. So we need three of something in order for it to come out. So three of any factor. So let's take 990 and let's break it down. So if we had 990, that would be 10 times 99, 10. The factors of 10 are two times five factors of r nine times 11 and the factors of nine R three and three. And that is as simplified as that one gets. We've got our factors of two times 3 squared Times five times 11. Not all equals 990, but there's nothing that it has three of inside of there. There's nothing that can come out cleanly and purely but there is that three squared and we know that we could say three squared. Well when we take the cubed root of three squared from previous lessons, we know from the rules of exponents that this is the same thing as three To the 2/3. So we can bring that three squared out and we can say that that is three to the two thirds times the cubed root of everything that didn't get to come out. So two times five times 11 then we can go ahead and do that math what is two times five times 11? Well that is 110 and we look at our answer choices and this matches with answer choice. D. Well done. We'll catch you on the next one.

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