in-3-38-write-each-expression-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-n-20

Question

In $3-38$ write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.
$$
x \sqrt{600}-2 \sqrt{24 x^{2}}+4 x \sqrt{96}
$$

Finian Lickona · Accepted Answer

All right, So for this exercise, we&#x27;re going to be simplifying the expression X Times radical 600 minus two. Radical 24 X squared. Hoo boy plus four x radical 96. Okay, so the first thing we&#x27;re gonna do is try to simplify this radical right here, notice that we can rewrite it a six times 100. 100 is the perfect square of 10. So we&#x27;re just gonna rewrite this as 10 Ex radical six. We can rewrite this 24 as four times six. And this X squared is already a perfect square, so we can factor that out. So if we factor this four outside of the radical we get, I&#x27;m gonna bring that to down times to the ex, gets factored out of the radical, and we are left with a six under the radical plus four X. And then this 96 can be rewritten as six times, actually. What? ISS 96. I swear I&#x27;m gonna math. Okay, anyways, so it&#x27;s not 18. It&#x27;s six times 16. So 16 is obviously a perfect square, and we can factor that outside of the radical as four. So we&#x27;re actually gonna include a times four right there and that six days inside the radical. So we really have Here is 10 x minus four X plus 16 x and they&#x27;re all times radical. Six. And if we simplify this 10 plus 16. 26 minus four is 22. So our final answer is going to be 22. Ex radical six.

Finian Lickona · Answer

So in this exercise, we&#x27;re going to simplifying the expression three X to the third re 80 plus to route 125 x two of sixth. So the first thing I&#x27;m gonna do is try to simplify this radical a little bit more. I see that I can recreate this as five times 16 so I can factor a four out of this radical and put that out in front here. So this is gonna become a 12 x to the third route five. So now I want to see how I can simplify this radical I c. I can rewrite this as that&#x27;s not going to be too as five times 25. And I can rewrite this as X squared times x squared times X squared. So if I factored this fi about that brings a a five outside of the radical on. And then all these X squared terms become one x cubed term outside of the radical, and I am left with a five inside the radical, which is what I wanted. So I have 12 x to the third over Route five and then two times five is 10 x to the third Route five. So our final answer is clearly going to be 22 x to the third Route five

Finian Lickona · Answer

So in this exercise, we&#x27;re going to simplify the expression Route 24 plus to route three halves. Now I want to get these radical terms to match. So I&#x27;m going to have to find a way to make this 24 look like a three halves. I can rewrite this 24 as 48 over to and now the denominators of both radical terms match. So what I&#x27;m really going to do is find a way to decompose this 48 into some perfect squares. So I recognize that I can rewrite this as three times 16 over, too. And this 16 right here could be factored out as a four. So what I really have is four times three over route two, plus two times three over route to which, of course, simplifies to six. No times radical. Three over two

Julie Silva · Answer

Praveen has to simplify the given expression. So the first thing they do is rewrite each of our radicals using the quotient rule, meaning I&#x27;m gonna take the square root of 1/6 and rewrite it as the square of the one over the square. The six, then for our second term, will rewrite the square root of eight thirds as a square that they over the square, the three and for our last term will rewrite it as the square of the two over the square of the three. All right, let&#x27;s see if we can simplify any. It&#x27;s radicals when the first fraction we have to square with one, which is one. So that&#x27;s just going to be one over the square of the six. Now, for a second fraction, we have the square of the V. Well, the perfect square four goes into it two times and the square of the forest to so this can be rewritten as 2/2. So we&#x27;ll have to root two divided by the square of the three. And then our last radical can be simplified. So we just have the square of the 2/3. I&#x27;m sorry the square of the three. Don&#x27;t want to forget that. Now, remember when we added subtract fractions, we need a common denominator. So take a look at these last two. We can combine them because they have the same denominator and the numerator we have to route to minus route two, which is just a square the to. So we&#x27;re gonna bring down 1/6. Plus, we have to square with the to all over the square root of three. Now we want to go ahead and try and combine these fractions, which means we need a common denominator, which in this case, will be the square root of six. So I&#x27;m gonna multiply our second fraction by the square of the two over the square of the two. Now we have the square with the two times the square of the two, which is two square before, and the square of the three times to square. The to is to square the six and then we&#x27;ll bring down our first fraction. We&#x27;ll take a look. Your new Marie. There you have the square of the four, but that&#x27;s equal to two. So we&#x27;re going to have one over the square, the six plus two over the square of the six. Now we have a common denominator. Let&#x27;s go ahead and combine those new Meridor&#x27;s well. One plus two is three. So we&#x27;re gonna be left with three divided by the square, the six, and now we can&#x27;t simplify fervor. So our final answer, like I just said, is three divided by the square of the six.

Julie Silva · Answer

we&#x27;re being asked to simplify the given expression. So the star, we&#x27;re gonna have to simplify each of these radicals. So let&#x27;s start with the square. The 12. Well, the perfect square four goes into it three times so we can rewrite this as to square the four Times square the three. Now, for our next radical, we have to square the 24 again. The perfect square four goes into it, but this time six times. So we write this as a square, the four times to square the six. All right for the square, the 48 the perfect square 16 goes into it three times. So we&#x27;ll rewrite this as to square the 16 times square the three. And for our last term, the perfect square nine goes into 27 3 times, so it will be rewritten as a square. The nine times square. The three. Now let&#x27;s go ahead and simplify well, the square of the forest to, and we can&#x27;t simplify to square the three, so we&#x27;ll bring that down. Next we have a square of the four again. It&#x27;s too, but you can&#x27;t simplify the square of the six. Next we have the square with 16 which is for And we can&#x27;t simplify the square of the three. And lastly, the square of the nineties three. And we can simplify the square of the three. So perfect. All of our radicals have now been simplified. Now we just have to combine any pairs of, like terms. Well, we have, like radicals that have radic cans of threes so we can combine all those coefficients. Well, two plus 46 and six plus three is nine. So that will give us nine. Route three and then we have minus two, Route six, which doesn&#x27;t have a late term. So we simply just bring that down. So now was simplified completely. So our final answer is nine or three minus two, Route six.

Finian Lickona · Answer

So in this exercise we&#x27;re going to be simple. Find the expression X times radical 32 x plus square root of 128 x to the third. It&#x27;s the first thing I&#x27;m gonna do is simplify this radical a bit more. I noticed that I can rewrite this as 16 times. 2 to 16 is a perfect square so I can factor that out as a four. So this becomes four x route to X. And now I want to see if I can make this radical become some term outside of it. Times radical to X. So I notice I can rewrite this X to the third is X squared Times X and I can rewrite this 128 as two times 64. 64 is a perfect square that comes up in front of the radical someone away that has eight. And the X squared comes outside the radical, too. And then I have to ex left inside the radical So four x times radical two X plus eight Ex Radical to X is obviously going to be four plus eight, which is 12 x radical to X. Our final answer is 12 ex radical to X

Problem

In $3-38$ write each expression in simplest form.…

Problem 22 Hard Difficulty

In $3-38$ write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.
$$
x \sqrt{600}-2 \sqrt{24 x^{2}}+4 x \sqrt{96}
$$

Answer

22$\sqrt{6} x$

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Educators

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

22$\sqrt{6} x$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry