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In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{\frac{8 x}{5 y^{3}}}$$

$\frac{2 \sqrt{2} x}{4{\sqrt{5}} y}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 3

Simplifying Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $3-38$ , write each rad…

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the square root of X over five y cube. Okay, this is equal to the square root of eight at eight. Axe AIDS X over the square root of five. Why pube? Okay, what a squirt of eight X. That's the squared of eight times. The square root of X squared of aid can be rewritten as a square root of four times two right times the square root of acts over while the square root of five y cube, I guess way written as the square root of wealth. Five. Why, um, we're both five y square times. Why, Okay, that's his five wise cube. But then, well, the squirt of four times two is quit of four times square to two, so the squid of four is too. So screwed of eight is equal to two times the square root of two. Because you have a product under your square root, you can go ahead and take the square root of a perfect square that can come outside of your radical, so the square root of four is too, so we're left with two times the square root of two. But then times the squirt of X. That's two times the square root of two X. And I know that this is equal to the square root of X. It's good of it. X is the square root of four times two times acts, so that's equal to two times the square root of two X. Okay, Divided by Well, uh, there's not much you can do here except for taking the square root of why square is just why. So that could come out. We have. Why times the square root of five wine. All right, all right.

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