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In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.$$\sqrt{\frac{a}{3}} \cdot \sqrt{\frac{a^{2}}{4}}$$

$\frac{a}{6} \sqrt{3 a}$

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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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in this problem we're solving for the square root of a over three times the square root of a squared over four. And for this problem, I'm gonna choose to simplify this term on the right first, because I noticed that both the top and the bottom are perfect squares. So this leaves me with the square root of a over three times the square root of a squared who were square root of four. This is equal to the square roots of a over three times A over to now in to deal with this term on the right. To do that, I'm going to similarly separate it into a top and bottom. So and I'm gonna put this term out in front just because I'm done dealing with it. So this is equal to a over two times the square root of a over the square root of three. Now, to get rid of this three on the bottom, when you do is multiply this term in particular by Route three over route three. Now, Route three over Route three is just a form of one. So we're not fundamentally changing the equation at all were simply multiplying by one. But what that does is that kids get gets rid of the radical on the bottom here with those route threes. So this is going to be equal to a over to times Route three A. From combining the three and a there divided by route three times, Route three, which is just three now if I bring this on to another line and multiply altogether, this gives me a Times Route three a divided by two times three. So this is equal to a over six times Route three A and that is our final answer.

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