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

$2 x^{2}$

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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 X cubed times the square root of four X. And to do this, we need to know that the square root of a times the square root of B is equal to the square root of a times B for A and B are any positive numbers. So in this problem here, we can combine into one big radical as thes square root of X Cute times four x to the one, and I add that one is an exponents to help with our next step. Where we combine these variables to multiply, execute an extra the first together we add their exponents. So we get the square root of X to the three plus one times four, which, including if we move for up to be our coefficient is equal to the square root of four X to the fourth. Now we're gonna use this processing green, but we're gonna go backwards. So taking this to another line this will be equal to the square root of four times the square root of X to the four. We've just broken up this radical right here. Our final answer is going to be equal to the square to four, which is to tens of square root of X to the fourth, which is X squared, and that's our final answer.

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