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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.$$\sqrt{\frac{4 a^{3}}{27 b^{3}}}$$

$\frac{2 a \sqrt{a}}{3 b \sqrt{3b}}$

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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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we have a square root of for a cube over 27. Be cute so well, we can rewrite this as two square root off for a cube over the square root of 27. Be cube okay, And then, while the square root of for a cube that's the square to four times the square root of a cube, the square to four is a perfect square that's equal to this is equal to two times, while the square root of a cube over what, a square 27 B cube that's equal to the square. Root off 27 is nine times three. Okay, times be cube, but it's got a nine history, so this is equal to two square root of a cube over square. Tonight is threes that can come out of outside the radical. We've got three, and we still have a three left. Inside the radicals, we have three times the square root off three b que. I guess we could go one step further here and say, Well, a cube is really a square times A. But in the square root of a square is a so we have. This could be equal to two times the square root of eight. Some excess because good of a cube is well, It's the square root of a squared times the square root of a but the square a square is a salt lips. So when a should come out here and age can come out, you have to a times the square root of a okay over well, three times the square root of three b cube. But again, be cube is B squared times B. We can pull out the square root of B square, which is be so what? We have over three B and then under the radical, we still have a three beat. So we have to a squirt of B over three b times the square root of three. All right, take care.

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