in-11-38-evaluate-each-expression-in-the-set-of-real-numbers-sqrtfrac4936

Question

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

Dilip Paruchuri · Accepted Answer

All right. Hey, Goes in this problem were given negative square root of 49 over 36 we&#x27;re being asked to simplify this expression and our answer. That problem states that are answers should be something that&#x27;s in the real numbers. So our answer should be a number in the rial number plane. So first, let&#x27;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&#x27;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&#x27;s equal to six squared, so our denominator becomes square root of six of whips. Mother, it&#x27;s gonna be the square root of six squared. And what will you will stick our negative son in front of it because that&#x27;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&#x27;re just getting that something. And since when we take the square root, we&#x27;re taking the principal square Root were only carrying up, but about the positive Valium. We only care about the positive seven that&#x27;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&#x27;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&#x27;re just writing out the square root that&#x27;s given in the problem, the problem always indicates that it&#x27;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&#x27;d have to consider the case of the positive negative seven, which really doesn&#x27;t matter in this case, because once again, principal Square root. And just to recap, our answer is negative. 76 Thanks for.

James Kiss · Answer

we were asked to find the cube root of 27. The Cuban of 27 is equal to the cube root of three cubed three to the 3rd 3 to the third is 27. We want to write 27 as a perfect cube so that our Q route and our cube counter Act one cancels the other. And so we&#x27;re just left with three. The cube root of 27 is three.

Dilip Paruchuri · Answer

Hey, guys. So this problem, we&#x27;re gonna try to find the square root of 1.44 when a quake multiplication thing that we&#x27;re gonna go over before we start. This problem is that 1.44 is equivalent to 1.2 times 1.2. And that&#x27;s the same thing as 1.2 squared. And as you guys might have guessed, that&#x27;s the same thing as negative 1.2 squared as well. Just a protest that we didn&#x27;t need to know that we&#x27;re gonna need in order to solve this problem. So we have the square root of 1.44 when we know that equivalent to 1.2 squared or a negative 1.2 squared. So, in a sense, one point this value can either be plus or minus 1.2. But since in most of these problems one we&#x27;re talking about the square root. Like I said in the previous videos, were considering the principal squirt. And when we&#x27;re Prince considering the principal square, we&#x27;re only considering the positive value. So on Lee, let&#x27;s just about again. We&#x27;re only considering the positive value of what the squared is equal to, and so are square 1.44 Since we&#x27;re only considering, the positive value is equivalent to 1.2. That is what this expression, that is what this expression simplifies itself to.

James Kiss · Answer

there has to find the Q Route of 8 27th This would be equal to the cube root of to to the third over three to the third because to to the third is equal to eight. Three to the third is equal to 27. We should have a goal of writing our values in perfect cubes so that our cube root can cancel our perfect cubes, leaving us with 2/3. It&#x27;s the cube root of 8 27 is to third&#x27;s.

James Kiss · Answer

were asked to evaluate the square root of 16. The square root of 16 is the same as that the square root of four squared because four squared is equal to 16 square roots and squares are in versions of each other, so they counter act. So when looking at this as the square root of four squared, it&#x27;s the same thing is four for is our answer.

James Kiss · Answer

we were asked to evaluate the negative square root from 16. The negative spirit of 16 is the same as the negatives. Gray route of four squared because four squared is the same as 16. And now, since square roots and squares are inverse, is the square root in this fair? Cancel each other out, so we&#x27;re just left with negative or and that is arranged.

Problem

In $11-38,$ evaluate each expression in the set o…

Problem 26 Hard Difficulty

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

Answer

$-\frac{7}{6}$

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$-\frac{7}{6}$

Algebra 2 and Trigonometry

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