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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? Explainwhy or why not.b. If you agree with Sarah, for which values of $a$ is the statement true? Explain.

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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Chapter 3

REAL NUMBERS AND RADICALS

Section 2

Roots and Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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Okay, guys. So in this problem, we're we'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's what she'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'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'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't obviously, but so let's take a look at why it'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's always defined. That's always defined. That'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's take a look at a less than zero if A'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't have something squared equaling a negative number, and as a result, the values of a and don'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'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'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't work and why this doesn't work for all values of a

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