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

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.
$$
\sqrt{2}+5 \sqrt{2}
$$

Julie Silva · Accepted Answer

for being asked to simplify the given expression. So we have the square with the two plus fiber to will remember, you can combine like radicals if they have the same radic. And in this case, because our Braddock an for both of our radicals are too we can combine these these air like radicals. So all we need to do is combine the coefficients. Remember, In the first radical to square, the two is coefficient is one So we&#x27;re gonna combine the coefficients. So we have one plus five, which is six. And then we bring down our radical the square the to. So our final answer is six route to

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

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

Finian Lickona · Answer

So in this exercise we are going to write six radical five minus four radical five in its simplest terms, our simplest expression. So because these ah both have the same radical terms, we essentially treat these like they are identical variables, just like you would say, six X minus four X That&#x27;s not actually relevant to the problem right there. I just wanted to demonstrate it for usability purposes so we can do the same operations as if we were doing operations on variables with coefficients. So essentially six Route five minus four Route five is six minus four times Route five, which is just simply going to be too Route five.

Julie Silva · Answer

we&#x27;re being asked to simplify the given expression. So we have to square the five plus the square root of 1/5. Well, let&#x27;s take a look to square with 1/5 and I&#x27;m going to simplify this off to the side. So the square with 1/5 Well, this can be rewritten as the square with one divided by the square of the five. And we know the square of the one is one, and we can simplify the square of the five. So we&#x27;re gonna leave that as is so now I&#x27;m going to substitute this expression in place off the square root of 1/5. So when I do that, I&#x27;m gonna have the square of the five plus one over the square of the five. Okay, Now we&#x27;re being asked to add, but we can only add when we have a common radical. And not only that, we also have a fraction. And remember, to add fractions, you need to have a common denominator. So in this case, are common denominator will be the square with the five. So I&#x27;m going to first off, take my first radical to square the five and put it over one, so it&#x27;s a fraction. And so that way they have the same denominator. I&#x27;m gonna multiply it by the square of the five over the square of the five. So now we have to square with the five times the square of the five, which is square, the 25. And in denominator, we have the square of the five times one which is just to square the five. And then we&#x27;ll bring down one over the square of the five. So perfect, they have the same denominator. Now take a look. Your first fraction, you have to square with a 25. But that&#x27;s just equal to five. So we&#x27;re gonna have five divided by two square, the five plus one over the square of the five. Now we have a common denominator. We can combine our two fractions. Well, when we add our new Meridor&#x27;s, we have five plus one, which is six. And then we keep the same denominator. And now we&#x27;ve simplified completely. So our final answer is six, divided by the square of the five

Julie Silva · Answer

we&#x27;re being asked to simplify to given expression. So we have eight or three plus the square of the three. Well, these air considered to be like radicals because both radic ans are the same. So we just need to combine the coefficients now for that second radical. The coefficient of the square of the three is one. Remember, when you don&#x27;t see a coefficient, it&#x27;s always one. So now we&#x27;ll just combine our coefficients. So eight plus one is nine, and we&#x27;ll bring down our radical the square of the three, so our final answer is 93.

Problem

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

Problem 3 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.
$$
\sqrt{2}+5 \sqrt{2}
$$

Answer

6$\sqrt{2}$

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6$\sqrt{2}$

Algebra 2 and Trigonometry

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Ann Xavier Gantert

Algebra 2 and Trigonometry