a-sarah-said-that-in-the-set-of-real-numbers-sqrta-is-one-of-the-two-equal-factors-whose-product-is-

Question

a. Sarah said that in the set of real numbers, $\sqrt{a}$ is one of the two equal factors whose product is $a .$ Therefore, $\sqrt{a} \cdot \sqrt{a}=a$ for some values of $a$ . Do you agree with Sarah? Explain
why or why not.
b. If you agree with Sarah, for which values of $a$ is the statement true? Explain.

Dilip Paruchuri · Accepted 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

M S · 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

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

Ankit Gupta · Answer

we have given question that is, we have to explain why you is a quarto for any deal numbers as this can be. Two dinners a couple a B to the Power Wonder goodbye in which can be getting us into the boat. One divided in multiply they be to the boat one divided by So it can be a Guinness because this Amy Toby under this must be a positive value. This is the product of a B must be a positive value, some lovely for these, a must be positive. L and B must be positive eloped that then only this under route will hold good that it&#x27;s a and B. It&#x27;s positive, all of which so you end these positive, the protective A B is always positive. So this really isn&#x27;t whole school for any D&#x27;Alemberte if this is a real number, because it must be a positive because under rude value cannot be negative. So for any real number, this and this this relation holds good. It can be also proved approved in this

Anna Jones · Answer

the given statement in this problem involving radicals of quantities that are being multiplied is actually stating the product rule. Thus, we know for sure this statement is true. So, for example, if we say a equals three and B equals two, well, and then we can say n equals Tuas Well, so it&#x27;s like the square root. So the square root of three times the square root of two is thus equal to the square root of six. If we check this in our calculator, we know for sure that this is indeed true.

Anna Jones · Answer

um this problem is actually a direct replication of the quotient rule. So if we were to take an equal to to a equal to four and be equal to nine and we substitute these values in, we would have the square root of four over the square root of nine equal to the square root of for over nine. Well, the square would have forced to the square root of nine is three. So we have 2/3. We also know that for ninth this is equal to 2/3 times 2/3. So when we think of this whole fraction taking the square root of that, we know that the answer is 2/3. Thus, these two sides are equivalent proving that this statement in this problem is true. So yes, this is true. It is stating the quotient rule.

Problem

In $3-10,$ tell whether each represents a number …

Problem 2 Medium Difficulty

Answer

a)Yes. The question is asking about SOME values, so we will replace a with the numbers 4 and 9 to show that some numbers do abide by this.
The reason it says SOME, is because this only applies for the square root of positive numbers. If we replace a with -4 and -9, this rule doesn't apply.

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Ann Xavier Gantert

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a)Yes. The question is asking about SOME values, so we will replace a with the numbers 4 and 9 to show that some numbers do abide by this.The reason it says SOME, is because this only applies for the square root of positive numbers. If we replace a with -4 and -9, this rule doesn't apply.

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

a)Yes. The question is asking about SOME values, so we will replace a with the numbers 4 and 9 to show that some numbers do abide by this.
The reason it says SOME, is because this only applies for the square root of positive numbers. If we replace a with -4 and -9, this rule doesn't apply.

Ann Xavier Gantert

Algebra 2 and Trigonometry