in-3-29-write-each-quotient-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-non--9

Question

In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. 
$$
\frac{\sqrt{35 a^{3}}}{\sqrt{10 a}}
$$

Matt Gibson · Accepted Answer

simplify a problem that has a radical in the numerator and radical in the denominator. I&#x27;m going to write it as one big radical. So dividing to radicals is the same as having one giant radical about with both inside. Now it&#x27;s easy to see that I can reduce. So five goes into the numerator five goes into the denominator. So I wind up with, um, five years into that seven times five goes into the denominator. Two times I reduced my A cube and divide by the A in the denominator leaves me with a square. Now I can&#x27;t have a radical in the denominator, So I have to rationalize this denominator by multiplying the top and bottom by the spirit of to anything divided by itself is one. So I&#x27;m allowed to multiply this by one in the numerator. I now have a square root of 14 a squared in the novel dinner. In the denominator I have the squared of four, which is just to our goal was to rationalize the denominator squared of a squared is a so I wind up with a times the square root of 14 divided by two

M S · Answer

So you have scared to 50 times a cubed divided by screw of 58 So the person want to do is write this infraction for so have scary with 50 a cute over skirt of five day so I can write this undo one radical And when we do that, we can cancel maker reduces fraction the numbers. So you beat that attorney to attain and five divided by five meetings more from their councils. So we have soon a cute over a And whenever we have the same based and we&#x27;re subtracting and we&#x27;re dividing So let&#x27;s say we have thanks to the a divide about exited beat and we have the same base. This just means we&#x27;re going to subtract the explanation So we haven&#x27;t understood exploitative or in here. So three months, one day out of the once too. So what happens? Girdwood saying I swear. And if you separate these, you know, screw teams on the spirit of a square and this radical cancel out with that swear So we have a time to spread its aim

M S · Answer

we want to express this In the simplest form, some little combine them to have one radical. So how 12 a square over for a So the numbers. I&#x27;m just going to divide them by the greatest common factor in this case it&#x27;s for So it&#x27;s low Divided by four gives us three and four divided before we give us one. So have to square a three a squared over a and you&#x27;ll notice that we have the same base here. So whatever we have the same base, the different exponents. We&#x27;re going to subtract er exponents. So this is spirit three and A to the two minus one. You two minus one just gives us one. So just seems to square, huh? Three A.

Matt Gibson · Answer

when I have a binomial divided by a mono meal. Two terms in the numerator divided by one term in the denominator. This is the same is dividing both terms in the numerator, by the denominator, it subtraction in the middle. So I need to keep that subtraction. Now. I just divide and reduced the image or parts and the radical parts. So in the first term I can cancel, reduce, and then five goes into 10. This is the same as having the square root of 10 divided by five. It&#x27;s the same thing, so that simplifies to be just the square to to I do the same thing Over here. The three of the nine reduce the five in the 50 reduced debate winds up giving me the square root of so three. The nine divided by three and then square to 50 divided by the square to five, gives me the squared attempt to my final answer.

M S · Answer

So we have this expression, everyone to simplify it. So the first thing we should do is combine needs to have the same radical. So we have the fourth root of a tongue Sweets of the port over a square, time to be to the port. So if you can recall well yet whenever we have the same base with different exponents, we had ups attracting those exponents so we can use that to simplify our variables. So have a to the one minus two. You have understood one here times B to the four minus four so we can simplify this Freddie. Well, Minister gives those negative for and foremothers forgives us here. So if you can also recall anything to zero power gives us boy so that automatically counsel. So the inside will live with this. Very, uh, the four through. Okay to the negative points. However, we never wanted to give you explain what separate Buying. So this is really one over 8 to 1. We get to the elevator, so get that positive. So this looks simplified, but we have to take a few extra steps, so you fully simplify. So we have the 431 over a. But the fourth fruit of wine will give us points, so that top was simplified. But we&#x27;ll have a radical and are denominated. And we don&#x27;t want that someone to try to make this pretty while we have these radical here last night Make it pretty. That means because we have this four only outside we went our bottoms, so you have the same result. And the only way can do you get it is therefore most part that&#x27;s hopping bottom. But thank you. I want to get rid of that radical and development is ever going to be Look what? So I remember whenever you multiply it and they have the same base gonna add the explanation notices a plus B. So in our radical would have a cube over, and this is a T the one plus three. We&#x27;ll just turn into radical of a cube over a to the fourth power. So if you simplify this further, we can have the fourth room. Ah, a cube over or okay to the board&#x27;s power. And this fourth power in this Radicals of the fort will counsel Orla with four crew. Uh, thank you over a. So the reason we could not leave it as but board root of one over a was because our numerator would have reduced the one so we would have had one over the fourth rule of Hey. However, it would have been tricky to try to rationalize it as that. And we would have still had to end up at this step here. So I just wanted to say was a few extra steps. Those want to show you that I&#x27;m not leaving us the fourth rid of whatever a because it was not fully simplified. So this is our answer here.

Matt Gibson · Answer

when I simplify a binomial Bayamon a meal, I need to understand that I have to divide each term in the numerator by the denominator. This is addition. So I still have addition here when I continue when I have a radical divide by radical, that&#x27;s the same as having one radical with both parts inside that radical. I don&#x27;t have to write that step. And I think that does make it easy to see. I reduced the tens, gives me the squared of one. Plus it reduced. These both divide by five. So this word of one is one. But I&#x27;m not allowed to have a radical in the denominator. So I need to rationalize this denominator here. I can multiply any number by one, and it doesn&#x27;t change the value. So the squared of two divided by the square to is really like multiplying by one. It changes what it looks like, but it doesn&#x27;t change my value. So this half then winds up being plus this word of three times square to give me the squared of six the square to Times Square to to use me. This where 24 which is just too, and

Problem

In $3-29$ write each quotient in simplest form. V…

Problem 11 Medium Difficulty

In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.
$$
\frac{\sqrt{35 a^{3}}}{\sqrt{10 a}}
$$

Answer

$\frac{\sqrt{14}}{2}$

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$\frac{\sqrt{14}}{2}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry