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In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.$$(x-\sqrt[4]{3 y})(2 x-\sqrt[4]{3 y})$$

$2 x^{2}-3 x \sqrt[4]{3 y}+\sqrt[2]{3 y}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 5

Multiplying Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $3-41$ , express each p…

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So we have X minus or Route three. Why? Tux to X minus four, Route three What? Someone of all the same process of boiling. So you multiply the 1st 2 We have two expired the outer terms. So have minus X times four through. Uh, do you want the inner terms? So we have two x times of 43 there you are. And they're gonna multiply the lasting terms they will have before through the three. Why times four critically. Why? Since it's the same thing conduced square, that So now we will do simplified further. So because these have the same base, we can combine the coefficient. So this is the negative politics, and this is a negative to it We're gonna bring down is to x squared and the negative 11 is to give us negative three x So I support through a 31 And with this last term here, this square, usually it cancels out with our radical. But because we have a four here, we divide or bar too. So just become spirited three wives. So in case it, you need a further explanation, let's plug in a simpler example. So let's say the 432 16 squared. This is really the fourth through of 16 times of 43 to 16. Now we know that the board through the 16 is, too, because two times, two times, two times to give us 16. So this is two times two and never give us four. So this shows that the radical does not just cancel out completely, but we just have to divide it by two. But that's how this radical is still here, and this is our final answer, as we cannot simplify it for this.

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