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In $3-38$ write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$x \sqrt{600}-2 \sqrt{24 x^{2}}+4 x \sqrt{96}$$

22$\sqrt{6} x$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 4

Adding and Subtracting Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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All right, So for this exercise, we're going to be simplifying the expression X Times radical 600 minus two. Radical 24 X squared. Hoo boy plus four x radical 96. Okay, so the first thing we're gonna do is try to simplify this radical right here, notice that we can rewrite it a six times 100. 100 is the perfect square of 10. So we're just gonna rewrite this as 10 Ex radical six. We can rewrite this 24 as four times six. And this X squared is already a perfect square, so we can factor that out. So if we factor this four outside of the radical we get, I'm gonna bring that to down times to the ex, gets factored out of the radical, and we are left with a six under the radical plus four X. And then this 96 can be rewritten as six times, actually. What? ISS 96. I swear I'm gonna math. Okay, anyways, so it's not 18. It's six times 16. So 16 is obviously a perfect square, and we can factor that outside of the radical as four. So we're actually gonna include a times four right there and that six days inside the radical. So we really have Here is 10 x minus four X plus 16 x and they're all times radical. Six. And if we simplify this 10 plus 16. 26 minus four is 22. So our final answer is going to be 22. Ex radical six.

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