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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.$$\sqrt{\frac{6}{81 y^{6}}}$$

$\frac{1}{9 y^{3}} \cdot \sqrt{6}$

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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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Okay, So should we have the square root of 6/81 y two e six now realize that this could be well split up as the square root of sex over the square roots of 81. Why? To these sex? Okay, now square six. Well, can I make six as the product of two numbers such that one of the numbers is a perfect square. Well, no, right. Six is either six times one with three times, too. But I don't have any perfect squares. So square to sex. I can't lead break up. So square to six is gonna remain escort of sex, but squared of anyone times wide to the sex when this is the square root of 81 times the square root of why to six. And it's good of anyone is nine. This is equal or divided by nine times. Well, the square root of why? To the sex. That's why. Cubed, right? Because why, cube times y cube is why to the six. So, um, we have a squared of sex over nine. Why cute. All right. Um so So, yeah. I mean, if you want I mean, I guess you could rewrite this as one over nine y cube Times Square to fix, right? I don't get any simpler or not, but just realize that that's also equivalent here, I take care.

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