In Exercises 11–28, add or subtract as indicated. You will need t...

Question

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals.
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3³√24 + ³√81

Accepted Answer

Hey, everyone in this problem, we're asked to perform the addition of radicals. After simplification, the expression we're given is 23 multiplied by the fourth route of 48 plus 17, multiplied by the 4th route of 768. We're given four answer choices. Option A 126 multiplied by the fourth route of three. Option B 80 multiplied by the 4th route of three. Option C 114 multiplied by the 4th route of three and option D multiplied by the 4th route of three. We're gonna start by rewriting what we were given. So we have 23 multiplied by the 4th route of 48 plus 17, multiplied by the 4th root Of 768. Now, we want to simplify these roots as much as we can. Ok. So right now we have 48 in the first one. The fourth root of 48 is not going to give us a nice integer number. So what we wanna do is we want factor 48 into something that will give us a nice integer. When we take the fourth route and then another term. So we can write S3 multiplied by 16. Now the fourth root of 16, that's gonna be a nice integer number. That's gonna be two. We can do this for the second half of our expression as well. We have 17 and we have the 4th route of 768. Now, 768, the fourth route doesn't give us a nice integer, but we can factor it again as three multiplied by 256. Ok. In 256, the 4th root of that is going to be four. All right. So we've kind of broken these terms under this roots up. But how can we actually apply this route to each of those terms individually? What we call, if we have the nth route of two things multiplied together, say X multiplied by Y, we can write this at the end root of X multiplied by the end through of Y. OK. So if the things are multiplied together underneath our, our root and we can split up, take the roots individually and then multiply at the end. Yeah. So let's go ahead and do that. We can write this as 23 multiplied by the 4th route of three, multiplied by the 4th route of plus 17, multiplied by the 4th root of three, multiplied by the 4th root of 256. Simplifying some more. We have 23 multiplied by the fourth route of three. OK. There's nothing we can do to simplify the fourth route of three, the fourth route of 16. OK. We already mentioned this. This is going to be equal to two, OK. Two to the exponent four gives us 16. And so the fourth route of 16 is equal to two, then we have plus 17 multiplied by the fourth root of three. And again, that same term, we can't simp simplify. And then we have the fourth route of 256. And again, we mentioned this is equal to 44 to the exponent four is equal to 256. And so the fourth route of 256 is equal to four. Now, we can simplify a little more. We have 23 multiplied by two in this first half of our expression. So we can write this as 46 and then we are multiplying by the fourth root of three. Then in the second half, we're adding, we have 17 multiplied by four, which gives us 68 multiplied by the 4th root of three, we have 46 multiplied by the fourth route of three plus 68 multiplied by the fourth root of three, which gives us 114 multiplied by the fourth route of three. OK. When we add those together, and that is our simplified expression and we can't simplify any further. And that's what we were looking for. So we found the correct answer is multiplied by the fourth root of three, which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. 3³√24 + ³√81

Key Concepts

Radicals

Like Radicals

Simplification of Radicals

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