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In $3-38$ write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{24 x y^{2}}+\sqrt{54 x y^{2}}$$

5$y \sqrt{6 x}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 4

Adding and Subtracting Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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we're being asked to simplify the given expression. Remember, when you're adding radicals, you want to simplify both radicals first. So let's start with the first one. We have the square root of 24 x y squared. Well, I can simplify the square of the 24 because the perfect square four goes into 24 6 times. So I'm going to rewrite this as to square the four times the square, the six. Then I'm gonna leave X in its own radical and only why square than its own radical. Then I'll bring down our plus sign. And now let's take a look at our second radical. We have the square of the 54 x Y squared. Well, we can simplify the square of the 54 because the perfect square nine goes into it six times. So I'll rewrite this a square The nine Times Square The six again I'm gonna leave the square root of X in its own and I'm gonna leave. Why squared in its own radical? All right, so let's go ahead and simplify. Well, the square of the forest to and the square of the UAE square is Why now we can't simplify the square of the six or the square. The axe. So we're gonna leave that together inside the rattle. We're going down the plus sign. Now let's go to our next set. Well, the square the nine is three. The square of the Y squared is why. And again we can't simplify the square of the six or the square that X So we'll rewrite that in one radical. Okay, Perfect. Now both radicals, air simplified. And these two terms of like terms because both radicals have the same Radha can. So we simply need to combine the coefficients well, two y plus three y is five y. So we'll bring down five y and then we'll bring down our radical the square of the six X. So now we've simplified our expression. So our final answer is five y times the square root of six X

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