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

Question

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\sqrt{3} \cdot \sqrt{27}
$$

Sarah Wharton · Accepted 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.

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

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.

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.

Sarah Wharton · Answer

in this question. We&#x27;re multiplying together. Seven route A times five route A over nine to do so, we&#x27;re going to multiply first, the coefficient whole numbers seven times five and then we&#x27;ll multiply together the items inside the radical signs. So this expression is equal to seven times five, which is 35. Tend to the square root of a times a over nine. We need to remember that is the same thing is a over one. When we do so, we remind ourselves that we can multiply straight across. So I&#x27;m going to multiply eight times a and one times nine to get the next step 35 times the square root of a times a divided by one times nine. This is equal to 35 times the square root of a squared, divided by nine. Moving this onto a second line. I now know that I can break this route of a squared over nine into two separate radicals 35 times the square root of a squared, divided by the square root of nine. And we&#x27;re lucky because both a squared and nine are perfect squares, so this will be equal to 35 times a over three, and this could just be written as one Big Fraction, which is 35. A over three has our final answer.

Problem

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

Problem 5 Easy Difficulty

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\sqrt{3} \cdot \sqrt{27}
$$

Answer

9

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