in-3-38-write-each-expression-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-n-18

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.
$$
\sqrt{\frac{1}{2 x}}+\sqrt{\frac{1}{2 x}}
$$

Finian Lickona · Accepted Answer

So in this exercise we&#x27;re going to simplify the expressions radical one over two X plus a radical one over to X now, because both of these radicals are already exactly the same, I don&#x27;t have to do any manipulation on them to combine them. I just have to add their coefficients, which in this case are both one. So what I have is one plus one times radical one over to X which, of course, simplifies to too radical one over to X.

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

Finian Lickona · Answer

All right, So in this exercise, we&#x27;re going to be simplifying the expression 49 x cubed under a radical minus two. Ex radical for X. So we want to make this radical looks something like this radical. So immediately, we recognize that 49 is a perfect square, it seven times seven and then X cube can be re written as X squared times X. So we can fact with seven out in front of the radical and the X squared out in front of the radical and we are left with just an ex inside of the radical. And now we move on this particular radical term right here. Four is a perfect square, so we can factor that out, is it too? So this term becomes four ex radical. So our secondary simplified stages seven ex radical X minus four x radical X, and this is very easy to solve. So seven minus four means that our final answer simply three ex radical acts

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 we have the square of the 50 close to square the too well, they&#x27;re not like radicals. So what we need to do is simplify first. So let&#x27;s take a look at the square of the 50. Well, it&#x27;s not a perfect square, but the perfect square 25 goes into 52 times so we can rewrite this as the square of the 25 times the square the to. Now we can&#x27;t simplify the square with a two because no perfect square divides into it. So I&#x27;m just gonna bring it down. All right, let&#x27;s go ahead and simplify. Well, the square the 25 is five and the square this to can&#x27;t be simplified. So I&#x27;ll bring that down and then I&#x27;ll bring down our second radical, the square the to Now that both radicals air simplified, Now we can combine them because both rather cans of the same. So they combined them. We just need to combine the coefficients and remember the coefficient of the square. The two is one. Well, five plus one is six and then we&#x27;ll bring down our radical sign. So we have to square the to. So our final answer is six route to

Problem

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

Problem 20 Easy 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.
$$
\sqrt{\frac{1}{2 x}}+\sqrt{\frac{1}{2 x}}
$$

Answer

$\sqrt{\frac{2}{x}}$

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$\sqrt{\frac{2}{x}}$

Algebra 2 and Trigonometry

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