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.
______ ___
√4x - 12 + √x-3

Accepted Answer

Hey, everyone in this problem, we're asked to perform the addition of radicals. After simplification, the expression we're given is the square root of 16 K minus 64 plus the square root of K minus four. We're given four answer choices. Option A five multiplied by the square root of K -4. Option B five multiplied by the square root of 4 -K. Option C5 multiplied by the square root of K-plus 4 and option D three multiplied by the square root of K -4. We're gonna start by rewriting what we were given. So we have the square root of 16, K - plus the square root of K -4. So the second term, the square root of K -4, it's not really anything we can do to simplify this. There's no factors we can pull out. We don't know what K is. So we can't really simplify anymore there. In this first term though, you notice that we have a common factor of 16 between these two terms and we know the square root of 16 and we know that that's equal to four. So let's try to factor out that 16 and see what we get. So we're gonna have this square root of multiplied by K - plus the square root of K -4. And now we have this common K -4 in each of these terms. OK. So that looks good. That looks promising. It looks like it might be something we'll be able to simplify further. Now, for our first term under the square root, we have 16 multiplied by K -4. How can we deal with this? How can we simplify this? We know we can take the square root of 16 if we have two things multiplied together underneath our square root. So the square root of X multiplied by Y, we can write this as the square root of X multiplied by the square root of Y. OK. So we can split them up, take the square roots individually and then multiply the result together and applying this rule to our problem. OK. We uh our expression is equal to the square root of multiplied by the square root of K - plus the square root of K -4. OK. Simplifying further, the square root of 16 is equal to four. And so we get four, multiplied by the square root of K -4 Plus The Square Root of K -4. OK. Four multiplied by the square root of K minus four plus one multiplied by the square root of K minus four. Well, that's gonna give us five multiplied by the square root of K -4. And if you didn't see that right away, the A addition there, you can always factor out. So you could have factored the square root of K -4 and you would have been left with four plus one, which gives you that constant five. And so after simplification, our expression is equal to five multiplied by the square root of K -4, which corresponds with answer choice. A 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. ____ _ √4x - 12 + √x-3

Key Concepts

Radicals

Like Radicals

Simplification of Radicals

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