in-3-41-express-each-product-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-non-n

Question

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\sqrt{2} \cdot \sqrt{8}
$$

Sarah Wharton · Accepted Answer

for this problem we&#x27;re trying to solve for the square root of two times the square root of eight, and I&#x27;m problems like these. We need to keep in mind that the square root of any number, for example, a times the square root of another number, for example, B is always equal to the square root of their product or the square root of a times B. So the squared of two times the square to eight is equal to then. The square root of two times eight two times eight is 16 so this expression is equal to the square root of 16 squared of 16 could be simplified to equal for. Therefore, the answer. This question is for

M S · Answer

so I have the spirit of eight times the square root of 12. So if you want to simplify this, that really means you want to think about the factors of each number and factor out the part picks were said backers of eight. You have won eight in two and four and our four is the perfect where so we know that the square root of four is too. Now come in handy. In a second, we have someone do something with our 12. So think about the factors of 12 will have warning spoiled to in six and three and four. But we also have this perfect square here, bored So we&#x27;ll separate both of them. Those good of apes. We wouldn&#x27;t have that story before. And four times to gives us a and to separate our square root of 12. We&#x27;ll have our spirit before, and four times three is 12. So we can simplify straight for is to and every necessary to and story for again is to bring down this very three Sanam. Just wanna, since everything is multiplied almost wanna multiply our regular numbers so two times Cygnus four and they will still have the spirited suits on spirit of three. And we can simplify under that radical sometimes three who did this

Sarah Wharton · Answer

in this question, we&#x27;re trying to simplify the expression square root of eight times six plus the square root of two. To do this, we&#x27;re going to distribute, so I&#x27;m going to distribute the square root of eight to the six and the square root of two, which will equal the square root of eight times six plus the square root of eight times the square root of two. This will leave me with this word of eight times six rearranged as six. Route eight plus eight times. Two. We&#x27;ll go together in the same square root, so be the square root of eat times. Two. This could be simplified further as six Route eight plus the square root of 16. Now it&#x27;s time to simplify the terms in each of these radicals. We&#x27;ll start with the Route eight six. Route eight can be broken down specifically. Eight is made up of four times two. So six Route eight could be rewritten as six times the square root of four times two, which is six times the square root of four times the square root of two, which is equal to six times too times the square root of two which is equal to 12 route to so six Route eight becomes 12. Route to the square root of 16 is just four. So our overall final answer is six Route eight, which again is 12 route to plus the square root of 16 which is just four, So that&#x27;s our final answer.

M S · Answer

so we have to queue. Brutal, too. Time security. Four. So because they have the same radical, we can combine everything under the radical so you can have two times for and two times four is eight, and the Q crew debate is too. Cube root works just like the square root. So square root is like two times two to give with sport. But the cube root is two times two times two or to give us eight. That&#x27;s how that works.

Sarah Wharton · Answer

in this problem we&#x27;re solving for the square root of a over three times the square root of a squared over four. And for this problem, I&#x27;m gonna choose to simplify this term on the right first, because I noticed that both the top and the bottom are perfect squares. So this leaves me with the square root of a over three times the square root of a squared who were square root of four. This is equal to the square roots of a over three times A over to now in to deal with this term on the right. To do that, I&#x27;m going to similarly separate it into a top and bottom. So and I&#x27;m gonna put this term out in front just because I&#x27;m done dealing with it. So this is equal to a over two times the square root of a over the square root of three. Now, to get rid of this three on the bottom, when you do is multiply this term in particular by Route three over route three. Now, Route three over Route three is just a form of one. So we&#x27;re not fundamentally changing the equation at all were simply multiplying by one. But what that does is that kids get gets rid of the radical on the bottom here with those route threes. So this is going to be equal to a over to times Route three A. From combining the three and a there divided by route three times, Route three, which is just three now if I bring this on to another line and multiply altogether, this gives me a Times Route three a divided by two times three. So this is equal to a over six times Route three A and that is our final answer.

Sarah Wharton · Answer

in this question, we&#x27;re solving for the square root of 1/3 times the square root of 24. To do this, we need to know that the square root of any number a times the square root of another number B is equal to the square root of their product. This word of a times B So this I&#x27;m going to rewrite to be a little bit more fraction friendly. So this will be the square root of 1/3 times the square root 24/1. And now, keeping this principle in mind, we can combine this in tow one radical the square root of 1/3 times 24/1 to solve further, we multiply straight across. We multiply one by 24 we won&#x27;t apply three by one. So this is equal to the square root of 24. Divided by three. Bring us down to another line. This leaves us with the square root of eight because 24 divided by three is eight, and we might be tempted to stop here, but it can be broken down by doing this process in reverse by thinking of what to numbers multiplied together to equal eight, and we could use foreign too. So this is equal to the square root of four times two, which, when broken apart, is equal to the square root of four times the square root of two. Our final answer is going to be the square to four simplified, which is just too times route to which can&#x27;t be simplified anymore. And this is our final answer.

Problem

In $3-41$ , express each product in simplest form…

Problem 3 Easy Difficulty

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\sqrt{2} \cdot \sqrt{8}
$$

Answer

4

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