in-3-41-express-each-product-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-no-10

Question

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
(\sqrt{12})^{2}
$$

M S · Accepted Answer

so we have to square 2 12 squared. This one is really simple because square root and squared are opposites of each other. This very well. Just cancel out and we&#x27;re left with Swell. Another way to prove this is that the square to 12 Times Square to 12 and the square roots also cancel out. So it was Lawrence&#x27;s.

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

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.

M S · Answer

So we have one minus the square root of three. All squared. So this is really well in minus grader three. So it was one minus squared at three. So keep all that oil meant it. We have one times one. Would you get this one square 23 times one, and it&#x27;s negative. So it&#x27;s wearing a three that our inner times, and that&#x27;s another minus Square 23 do was parlors terms. So because they&#x27;re the same base, the radical would just cancel. And I needed times negative. King was positives that would have plus three here. So we&#x27;re gonna combine our normal numbers. So one plus three don&#x27;t get close four and then because we have the same base here and here, we can combine their coefficients of one. So negative one minus one will give us a negative too Spirit of three. And just as far as we can simplify it. Expression

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

for this problem, we&#x27;re solving three Route three squared, which can be expanded as three route three times three, Route three. To solve this, we multiplied together the whole numbers in front and we multiply the numbers inside the radical signs. So this will be equal to three times three times route three times Route three. This part, the three times three is equal to nine. And the second part here could be combined in the same radical as the square root of three times three. Bringing this down to another line. This is equal to nine times the square root of nine. We know that this word of nine is equal three. So this is equal to nine times three, which is equal to 27 that is our final answer.

Problem

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

Problem 12 Easy Difficulty

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
(\sqrt{12})^{2}
$$

Answer

12

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