in-3-29-write-each-quotient-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-non-14

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. 
$$
\frac{\sqrt{12 a^{2}}}{\sqrt{4 a}}
$$

M S · Accepted 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.

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.

M S · Answer

want to express this in simplest sport. So the first thing we&#x27;re gonna do is we&#x27;re going to separate the two, so don&#x27;t have to deport fractions. So we have four routes to over sue route, too, plus a route 12 over to root soup. So from the first faction, we noticed that this will counsel with this and for the numbers were wanted to divide them by their greatest common factor, which is to sew, to divide about she was blowing and board about about two gives us, too. So this first fraction simplifies into two for a second fraction. We&#x27;re gonna divide the regular numbers by their greatest common factor, which is to in this case, so eight, about about two gives us for ensued. About about two kids this point. So we also have to radicals that were dividing someone say for times, and I&#x27;m going to combine their radicals. So we have 12 over, too, and I&#x27;m Linda about the fractions, but its greatest from a factor which is to in his case, it&#x27;s worked out about, begins at six. And to divide about to use this bully. So under the radical will have six. So I have two plus four times its query dipstick

Matt Gibson · 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

Matt Gibson · Answer

So to simplify this problem when I have a radical divided by another radical, this is the same as having one big radical with the other two inside, which makes it easy to simplify. I can divide, since they&#x27;re both even 27 has a perfect square. This would be the same is nine times three, so this would be the squared of nine times the square to three, which simplifies to be three times the square root.

Problem

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

Problem 16 Easy 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.
$$
\frac{\sqrt{12 a^{2}}}{\sqrt{4 a}}
$$

Answer

$\sqrt{3 a}$

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$\sqrt{3 a}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry