in-11-38-evaluate-each-expression-in-the-set-of-real-numbers-sqrtx6-x-geq-0

Question

In $11-38,$ evaluate each expression in the set of real numbers.
$$
\sqrt{x^{6}}, x \geq 0
$$

James Kiss · Accepted Answer

where were asked you very the square root of X to the sixth. Well, Exodus Sixth can be written as X to the third squared. Since we&#x27;re taking the square root, we should try toe right, our expression as a perfect square. So ext of the third to the second is extra the sixth. So this allows us to cancel our perfect square with a square root. And this is X to the third so scared of exit. The sixth is except the third little going us for you here. Another way to see this is thinking of Skerritt of X to the sixth as being equal to X to the sixth to the 1/2 The power of 1/2 is the same thing as square rooting and power to a power we multiply our powers So six times 1/2 is three. So that&#x27;s worried of acts of the sixth again is X to the third

James Kiss · Answer

we&#x27;re pacifying the square root of 0.25 x squared. Since we&#x27;re square rooting, we should try to write our expression. In terms of perfect squares. 0.25 is the same thing as 0.5. I swear and X squared is obviously X square. There is a property with oh, radicals that allows us to break up a product. So this is the same thing as the square root of point five square times the square root of X squared. So this whole expression would be equal to, um once we account for our square roots. Counter acting are perfect squares in canceling them out 0.5 times x, so the square root of 0.25 x squared would be equal to 0.5 x.

James Kiss · Answer

were asked to find the Q route of zero 0.0 01 Well, thank you, Root no clean 001 is the same thing as the Cube root. A 0.1 to third 0.1 of the third is 0.1 Now that we run, it is the perfect Q Bar Cube root and are perfect. You counter act there in verses of each other, and now this tells us that the cube root of 0.1 is simply zero 0.1.

James Kiss · Answer

were asked to find the positive and negative square root of 0.64 This would be equal to the positive and negative square root of zero point Eat Square. Because you&#x27;re a 0.8 squared is the same as 0.64 So this would be equal to the positive and negative. Um, 0.8. Because square roots in squares counteracted there in verses of each other you may want your answer is positive and negative, but this really is the same thing as separating it out with two solutions here, the positive 0.8 and negative 0.8. So the positive and negative skirted 0.64 is 0.8 and negative 0.8.

James Kiss · Answer

were asked to evaluate the negative fourth root be to the eighth over 1296. Since we are asked to find the four through Do we should be thinking about writing our expression in terms of perfect degree, for so Be to the eighth can be rewritten as B to the second to the fourth, be to the second of the fourth is the same as B to the ache. Likewise, 1296 is the same thing as six to the fourth. Now that we have read written our expression in terms of perfect fourth, our fourth root will cancel those out. So the negative four through toe be to the eight over 12 96 would just be equal to B squared over six and the negative of that because we started with in negative expression

Dilip Paruchuri · Answer

all right. Hey, guys. So, in this problem, we&#x27;re given the, uh, expression plus remind square with 16 were asked to simplify this expression and by now, what equals two And so first, let&#x27;s take away the plus or minus and just take a look at the square of 16. Now, in these type of problems, whenever you&#x27;re giving the square root, you&#x27;re being asked the principal square root. Now, the principal square root is the same thing as the positives were. Basically, it only takes in consideration of positive value. Now we know. So let me explain what that means. We know that 16 is equal to four square 16 is also equal to negative four squared as well, and when you take the square root of 16 it can either be four or negative for, But when you take the principal square root, you only consider the positive value here. So what happens is when you take the principal squared of 16 that&#x27;s equal to four. But since you&#x27;re taking plus or minus the square root of 16 plus or minus the principal squirt of 16 the squared of 16 is gonna superfight afford, but you&#x27;re still don&#x27;t have a plus or a minus in the front of it, so your actual answer is still plus or minus four. So this is what the expression plus or minus words 16 is equal to. Keep in mind the concept of the principal square root principal square root similar to the positive square root on Lee considers the positive value of what the square root is equal to. Thanks for listening, guys, and I hope this helps solve this problem.

Problem

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

Problem 31 Medium Difficulty

In $11-38,$ evaluate each expression in the set of real numbers.
$$
\sqrt{x^{6}}, x \geq 0
$$

Answer

$x^{3}$

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$x^{3}$

Algebra 2 and Trigonometry

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Algebra 2 and Trigonometry