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In $11-38,$ evaluate each expression in the set of real numbers.$$\sqrt[4]{0.0256}$$

0.4

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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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Hey, guys. So in this problem were given forth fruit of 0.256 and were asked to simplify this expression into a number or a value that's in the real numbers. So the first step we see that we're given 1/4 of route. The way we get rid of roots or fourth roots or any roots in general, is if we do the opposite. If we if we raise something to the X ray, something to that same power, meaning if you have the fourth route, if you take 1/4 root of something raised to the fourth power, the fourth route and that in the raising to the fourth Power cancels out and you're just left with the number. So basically, what I mean is, if you're taking the fourth, the root of let's Say X to the fourth, the fourth route and the four and the four in the exploding cancel out and you're just left with Simple X. And so we want to do the same thing in order to Ken throughout the fourth route, we want to write our 0.256 as something to the fourth power and threw some algebra. We see that points your tooth 56 is equal to 0.4 times itself four times. And I'm going to show you the algebra right here. So we have 0.4 times itself for times So 0.4 times zero point for is equal to 0.16 and 0.16 times 0.4 is equal to 0.64 And finally 0.64 times 0.4 is equal to zero 0.256 which is the value that we have in our expression. So what we could do is we could rewrite this expression as the fourth root of 0.4 to the fourth. Now, if you've been paying attention to squares and radicals, you all. You also can make the assumption that this can also be equal to the quantity negative zero point forward to the fourth as well. However, since when we're taking when a problem gives us the sport, the route when it explicitly writes down a root function, we always take the principal root, meaning we always consider the positive value of the radical but just keep in mind that points year 256 is also equal to the quantity of negative 0.4 to the fourth as well. Just that just that in this problem, we only care about the positive Because we're given the four through. That just implies that we take the principal route. So basically the fourth route and the, uh 0.4 to the fourth power, the fourth power and the four through it cancel out and you're just left with 0.4 so forth. Fruit of 0.256 is equal to 0.4, and we just included are positive value. Just keep in mind that this answer could have been negative. But since we're taking the principal route, we will. You just keep in mind that Ah, we have our positive value. Thanks for listening, guys. And I hope

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