In this Exercise Set, assume that all variables represent positiv...

Question

In this Exercise Set, assume that all variables represent positive real numbers.
In Exercises 1–10, add or subtract as indicated.
_ _ _ _
6√7 - ³√x + 2√7 + 5³√x

Accepted Answer

Hey, everyone in this problem, we're asked to perform addition or subtraction assuming that the variables are positive real number. The expression we're given is seven multiplied by the square root of 13 minus the Q root of Y plus six, multiplied by the square root of 13 plus nine, multiplied by the Q root of Y. We're given four answer choices. Option A, the Q square root of 13 plus multiplied by the Q root of Y. Option B, the square root of 13 minus eight multiplied by the Q root of Y. Option C 13 multiplied by the square root of 13 plus eight, multiplied by the Q root of Y. And option D 13 multiplied by the square root of 13 minus eight, multiplied by the Q root of Y. We're gonna start by rewriting what we were given. So we have seven multiplied by the square root of minus the cube root of Y plus six multiplied by the squared of plus nine multiplied by the Q root of Y. Now we wanna collect like terms, OK? Just like we would, if we had just a Y term, OK, just Y to the exponent one, how we would collect light terms and expression. We're gonna do the same thing. So let's start with our route 13 terms. OK? We have the square root of 13. And if we factor that from our expression, we have seven multiplied by the square root of 13. So we have seven and then we have plus six multiplied by the square root of 13. So we get plus six. So we have the square root of 13 multiplied by 7-plus 6. And then we're gonna add, and we're gonna add the cube root of Y multiplied by what? Well, we have a Q word of Y term here that's subtracted. So we have a negative one and at the end of our expression, we have plus nine multiplied by the cuber of Y. So we get plus nine. OK? So we're just collecting like terms here and factory. Now we can simplify the square root of multiplied by 7-plus 6. Seven plus six is going to give us 13. And so we can rank this as 13 multiplied by the square root of 13 in the next term. OK. The coefficient is negative one plus nine, that's gonna give us positive eight. And so we have plus eight multiplied by the Q root of Y. Now the square root of 13 that can't be simplified any further. 13 is a prime number. The key word of Y that can't be simplified any further either And so this is the simplified expression we were looking for, we found the correct answer is 13 multiplied by the square root of 13 plus eight, multiplied by the Q root of Y which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

In this Exercise Set, assume that all variables represent positive real numbers. In Exercises 1–10, add or subtract as indicated. _ _ _ _ 6√7 - ³√x + 2√7 + 5³√x

Key Concepts

Radicals

Like Terms

Combining Radicals

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