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In $43-46,$ solve each equation for the variable.$$a^{2}=196$$

$\{-14,14\}$

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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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In $43-46,$ solve each equ…

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Solve each equation. $…

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all right. Hey, guys, In this problem, we're giving the equation. A square is equal to 1 96 and in this problem there is no stipulation on what a is. So we don't know if A's positive. We don't know if it's a negative number. We clearly know it's not zero because you're squaring and you're getting, ah 1 96 so campy zero. But we don't know if it's positive. We don't know it's negative, and we're being asked to solve for the values of a So, basically, each operation mathematical operation has its opposite. When you're dealing with an equation in order, when you have something added to something the way you get rid of that, it is by subtracting it when you have a variable squared. The way you get rid of that with the square is a few square root boat sites, and that's what we're gonna do as our first test. We're gonna take the square root of both sides, and the square root of the left side is gonna we're gonna have squared of a squared square root of a squared is just a and then you have the square root of 1 96 Squared 1 96 is also is equal to 14 squared but also equals here negative 14 square. And since we're not taking the principal square, because when we say the principal, when I've talked about the principal square root in the previous problems, we assumed the principal square root because a problem gave us the square root. When the problem gives you the square root, most problems ask you to assume it's the principle square root. But in this case, we're square routing the pro. We're square, routing the number in one of the steps of our solution to the problem. So in that case, we can assume that we're taking the principal square root. We're just taking the square root, and when you're taking the square root, you have to consider all possible values off the square root. So in this case, this can either be 14 squid, the 1 96 another 14 squared or negative 14 squared, and when you take the square root of both the values that you get it plus or minus 14. And if you remember what I said in the beginning of this video that we don't have any stipulation on a We don't know if A's positive or negative. This is what I meant. I meant that they can either be a positive number or negative number because both of these values positive 14 and negative 14 make the initial equation a squared equals 1 96 True, and this is gonna be our answer won't have multiple answers to this problem. And that is positive. Negative. 14. Thank you for listening, guys. And I guess the one takeaway is that in this step, when we square root both sides, we're not taking the principal square root. And that's what gives us our multiple value answers. Thanks for listening.

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