in-3-41-express-each-product-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-no-11

Question

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

Sarah Wharton · Accepted 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.

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.

M S · Answer

So we have the port through of 27 time support, 3 to 3. So because the radicals are just saying, we can combine everything I need to radical so you can have 27 tons. Three. Only the radicals 27 times three Is this aging one and the fourth word of anyone fourth route, where it&#x27;s just, like swear route. But it&#x27;s four numbers board that four of the same numbers multiply together. And now to give us a tingly in this case, the fourth or debating Willingness. Three. That&#x27;s three times. Three times, three times three will give us a tea boy. So the fourth we&#x27;re debating witness three.

M S · Answer

So we have to square in 21 something spirit of 4/3. So one thing I noticed automatically is that if we split apart our second square root, so have a scary to four. On top of spirit of three, we can simplify our numerator. But I also noticed that three is a factor. 21 focus put apart our 21 We have skirted three times square to seven. So I&#x27;m screwed of four over square 23 Another square root of four is too. So we have three times. We&#x27;re seven times to over Route three. And since the rules applying, we can cancel this out with our three on the bottom, they&#x27;ll have to say I was a spirit of seven.

Sarah Wharton · Answer

in this problem we&#x27;re trying to solve for the square root of three times the square root of 27. Keeping in mind that the square root of a times the square root of B is equal to the square root of a times B, the original expression can be simplified to the square root of three times 27. Three times 27 is equal to 81 so this expression could be simplified further to the square root of 81. Now we&#x27;re lucky because the squared of 81 is a whole number, so this could be simplified to nine, which is our final answer.

Problem

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

Problem 13 Easy Difficulty

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

Answer

27

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