Evaluate each expression in Exercises 55–66, or indicate that the...

Question

Evaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ³√8

Accepted Answer

Hello today we're going to be working on simplifying a radical expression. So the radical expression given to us is the cube root of 1,331. Now. In order to start simplifying this. Let's go ahead and break up 1331 into a group of prime numbers or the product of prime numbers. More specifically. So 1331 can be broken up into 11 times 100 and 21 11 is a prime number. So let's just go ahead and circle that for now. Next 121 can be broken up as times 11 and now we have two more instances of 11 here. So we want to go ahead and take this and put it back into the Cube root. Doing so is gonna give me the cube root of 11 times itself three times or 11 raised to the third power. Now, rewriting this expo I'm sorry not to explain. Rewriting the Cube root is going to give me 11 raised to the third power. All of that race to the one third. Now we're gonna go ahead and apply our exponential multiplication here. And that's gonna give us 11. Race to the third power times one third And that's going to be 11 raised to the 3-3 power or better yet just 11 raised to the first power which is just 11. That means that our solution to this problem is going to be a so I hope this helps you simplify radicals that are very large. And I'll go ahead and see you all in the next video.

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