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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.$$\sqrt{\frac{1}{6}}+\sqrt{\frac{8}{3}}-\sqrt{\frac{2}{3}}$$

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

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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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Praveen has to simplify the given expression. So the first thing they do is rewrite each of our radicals using the quotient rule, meaning I'm gonna take the square root of 1/6 and rewrite it as the square of the one over the square. The six, then for our second term, will rewrite the square root of eight thirds as a square that they over the square, the three and for our last term will rewrite it as the square of the two over the square of the three. All right, let's see if we can simplify any. It's radicals when the first fraction we have to square with one, which is one. So that's just going to be one over the square of the six. Now, for a second fraction, we have the square of the V. Well, the perfect square four goes into it two times and the square of the forest to so this can be rewritten as 2/2. So we'll have to root two divided by the square of the three. And then our last radical can be simplified. So we just have the square of the 2/3. I'm sorry the square of the three. Don't want to forget that. Now, remember when we added subtract fractions, we need a common denominator. So take a look at these last two. We can combine them because they have the same denominator and the numerator we have to route to minus route two, which is just a square the to. So we're gonna bring down 1/6. Plus, we have to square with the to all over the square root of three. Now we want to go ahead and try and combine these fractions, which means we need a common denominator, which in this case, will be the square root of six. So I'm gonna multiply our second fraction by the square of the two over the square of the two. Now we have the square with the two times the square of the two, which is two square before, and the square of the three times to square. The to is to square the six and then we'll bring down our first fraction. We'll take a look. Your new Marie. There you have the square of the four, but that's equal to two. So we're going to have one over the square, the six plus two over the square of the six. Now we have a common denominator. Let's go ahead and combine those new Meridor's well. One plus two is three. So we're gonna be left with three divided by the square, the six, and now we can't simplify fervor. So our final answer, like I just said, is three divided by the square of the six.

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