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In $11-38,$ evaluate each expression in the set of real numbers.$$-\sqrt{\frac{49}{36}}$$

$-\frac{7}{6}$

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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 $11-38,$ evaluate each …

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All right. Hey, Goes in this problem were given negative square root of 49 over 36 we're being asked to simplify this expression and our answer. That problem states that are answers should be something that's in the real numbers. So our answer should be a number in the rial number plane. So first, let's get started. So the first thing that we want to do is we want to make the algebraic step of splitting up the radicals. So we know that square Route 49 over 36 is the same thing as the negative square root of 49 over the square root of 36. Now we just basically sweet this split the square root into the numerator and into the denominator. So now we take a look at our numerator. 49 49 is a perfect square. It's equal to seven squared, so the numerator becomes square root of seven squared and our denominator becomes we know Well, we know that 36 is a perfect score. Is that well, it's equal to six squared, so our denominator becomes square root of six of whips. Mother, it's gonna be the square root of six squared. And what will you will stick our negative son in front of it because that's what the problem gives us. So now we have expression negative of square root of seven squared over square root of six square. Well, when you take the square root of something, swear you're just getting that something. And since when we take the square root, we're taking the principal square Root were only carrying up, but about the positive Valium. We only care about the positive seven that's gonna come out of the square root. So our top is just gonna become seven. And our bottom is just gonna become six. And we have the negative sign out front. So, as you can see, right here are negative square. Route 49 over 36 becomes negative seven six. And so our answer is negative. 76 That's what this radical right here, um, simplifies to And just to recap, what important step right here is that when you take the square root, when when we're just writing out the square root that's given in the problem, the problem always indicates that it's ah, principal square root. So we only care about the positive value that the square Valley leads to key step, because otherwise we get negative seven. We'd have to consider the case of the positive negative seven, which really doesn't matter in this case, because once again, principal Square root. And just to recap, our answer is negative. 76 Thanks for.

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