in-3-41-express-each-product-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-no-13

Question

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\sqrt{x^{3}} \cdot \sqrt{4 x}
$$

Sarah Wharton · Accepted Answer

in this problem we&#x27;re solving for the square root of X cubed times the square root of four X. And to do this, we need to know that the square root of a times the square root of B is equal to the square root of a times B for A and B are any positive numbers. So in this problem here, we can combine into one big radical as thes square root of X Cute times four x to the one, and I add that one is an exponents to help with our next step. Where we combine these variables to multiply, execute an extra the first together we add their exponents. So we get the square root of X to the three plus one times four, which, including if we move for up to be our coefficient is equal to the square root of four X to the fourth. Now we&#x27;re gonna use this processing green, but we&#x27;re gonna go backwards. So taking this to another line this will be equal to the square root of four times the square root of X to the four. We&#x27;ve just broken up this radical right here. Our final answer is going to be equal to the square to four, which is to tens of square root of X to the fourth, which is X squared, and that&#x27;s our final answer.

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 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

you have to square It affects summer to Times Square. That expired over too. So the first thing I want to do is I&#x27;m going to split apart the radicals. So we have a spirit of X over the spirit to time screw of X squared over this swearing too. So our talk this square Uranus squared were canceled. Still have it times the spirit of it. Oh, we&#x27;re our denominator and a spirit of two times greater too will give us two. And that&#x27;s a CE faras. We can simplify this expression.

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.

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.

Problem

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

Problem 15 Easy Difficulty

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\sqrt{x^{3}} \cdot \sqrt{4 x}
$$

Answer

$2 x^{2}$

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$2 x^{2}$

Algebra 2 and Trigonometry

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Algebra 2 and Trigonometry