jennifer-said-that-if-a-is-a-positive-real-number-then-sqrt4a2sqrta-do-you-agree-with-jennifer-justi

Question

Jennifer said that if $a$ is a positive real number, then $\sqrt[4]{a^{2}}=\sqrt{a} .$ Do you agree with
Jennifer? Justify your answer.

M S · Accepted Answer

So Jennifer said that the fourth Roots, uh, a squared is the square root of a Do we disagree or agree? I agree, and I&#x27;ll show you what. So whenever you have the square root of a number will stay. In this case, there&#x27;s always been understood to here, and everything has an explanation. Boy. Already. So we want to write this with the fractional exponents will have a to the wood half. So another way to write our left hand side would have before three to base. We&#x27;re no other way to write this with Braxton. Explain it will have a report. Did you tell you the number under the house and put it over the number outside of the house. And to reduce that fraction, we&#x27;ll have a to the 1/2. And to rewrite that with a square root will help the square root of a and it is our right hand side. So we I agree

Matt Gibson · Answer

the question asks, if these are equal. You cannot divide a radical by an an edger, so these would not be equal. You could divide this with your calculator and you would see that these would not give you the same decimal. If I have this, that would give me the same as the square root of that which would give me the same thing. And clearly dividing by two is not the same as

Bahar Tehranipoor · Answer

in this exercise, we have that X corpse, be ecstasy is a polynomial and that this person, Rita, is saying that we only have real roots when B squared is greater than or equal to four a. C. And so this is a true statement. We agree with what Rita is saying because we&#x27;re doing the quadratic formula and we have opposite B plus or minus the square root of B squared minus for a seat over to a That&#x27;s our route. So when we have the script on this for a C for this route to be riel, this has to be greater than equal zero. So you could say B squared minus for a C Square than or equal zero and tow ad for a suitable sides we end up at B squared is greater than or equal to four a. C. So if this is true, it means that our roots are riel. So it Rita saying, is indeed correct

Dilip Paruchuri · Answer

Okay, guys. So in this problem, we&#x27;re we&#x27;re told the viewpoint of a student named Sarah and Sarah says that square with a is the only equal factor of the value. A and A is said to be an element of the real number, so just a real value. And she says that a square A is the equal factor of its meaning. A is equal to square with a type square with a squared A divides a evenly. Basically, that&#x27;s what she&#x27;s saying. And she says that this is true for thung values of A and the textbook. The problem asked us to say, Do we agree with this dude? What or don&#x27;t we? And it says If we do agree with that, say which values of A that this is true for and a key freezing. This problem is for some values obey because this some values of a could also be for all values A for non values of a or for some values obey. So let&#x27;s take a moment to understand what it means for some values today for some values of a means that some values work. Some bodies don&#x27;t obviously, but so let&#x27;s take a look at why it&#x27;s not true or it is true for all values of a. So when you think of all values of a A can either be greater than zero, they can either be equal to zero or a can either. Be a less than zero. Now, if a is positive, you and you take the square root of a positive number. You know that&#x27;s always defined. That&#x27;s always defined. That&#x27;s never gonna be incorrect but ends next step. If you say that a is equal to zero, you take the square root of zero. This is always true. Squared of zero is always zero, so this step is also true. So right now, what Sarah is saying works for a greater than our equal to zero. Now let&#x27;s take a look at a less than zero if A&#x27;s negative square root of a is undefined, so undefined. So the statement that a is equal to square with a touch where a is incorrect because a negative number cannot be something times another thing. You can&#x27;t have something squared equaling a negative number, and as a result, the values of a and don&#x27;t work is when a is less than zero. So, in a sense, Sarah is correct that it only works for value for some values. And the values that it works for is for values of a greater than zero. Assuming that A is an element of the real numbers and just to recap, we do agree with Sara&#x27;s. There is correct Skirt a R Squared A is an equal factor of a for some values of A and the values of A. That work is when a cz greater than or equal to zero. And that&#x27;s just to say again under the assumption that is a real value. Thanks for listening, guys hope this helps solve this problem. And I hope this helps with that theoretical understanding of square root of a negative number. Why that doesn&#x27;t work and why this doesn&#x27;t work for all values of a

James Kiss · Answer

Kevin says that if the index of a radicals, even in the Radicals, positive that we get to solutions, And for that we say Kevin is absolutely correct. Okay, here&#x27;s why Kevin is correct on this with RN Through of K, we get to solutions. Here&#x27;s a real example. If N is even like to in case positive, like nine, we have the square root of nine, and we know that the square root of nine is either. Three. You&#x27;re negative three for part B. Uh, coming says that if the Radic, if the index is odd in the radical, has a Onley one real root. And for this we should say that Kevin is correct again. Here&#x27;s an example. Why again, with the end through of K in this instance, either we have one route either a positive or a negative root. Let&#x27;s take an example of the cube root of eight. So N is odd, and K is positive. The cube root of eight is positive, too, whereas if K is negative, like the Cuba of negative eight that is equal to negative two. So we get only one solution. It depends on if K is positive or K is negative

Sarah Wharton · Answer

So our question here is that if we know that a 345 triangle is in fact a right triangle is three bird to forward to fiber to also a right triangle if we just take all these sides and multiply by route to and there&#x27;s a lot of different ways that we could answer this question. But the way I&#x27;m to do it is by comparing the ratios of the sides. So I&#x27;m going to label each side as a B or C just so we can map them together. Thes two are the same side. For example, the two that have the letter a um and so I&#x27;m gonna compare for the original right triangle will do it in green. A over B is equal to 3/4, and in our new triangle, the one that we think might be a right triangle. A over B is equal to three routes, two divided by four route to. But if we simplify, we realized that the two were choose just ah, they cancel out, leaving us with 3/4. So these are actually the same fracture, the same ratio. We can check the other sides to we could do be oversee that would be equal to 4/5 in our original triangle and in our new triangle, be oversee is equal to four Route two divided by five route to which the route twos cancel out, leaving us with four fifth. So that also shows us that those ratios air the same and we&#x27;ll just do the last one. For good measure, we&#x27;re gonna do the ratio of a oversee, which in our original triangle is 3/5. In our new triangle, a oversee is equal to three route to divided by five route to which you might be able to guess the root who&#x27;s cancel out to leave us with just three fifths. So using our method of ratios, we get the answer that, yes, this triangle is a right triangle.

Problem

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

Problem 2 Easy Difficulty

Jennifer said that if $a$ is a positive real number, then $\sqrt[4]{a^{2}}=\sqrt{a} .$ Do you agree with
Jennifer? Justify your answer.

Answer

Yes

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