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Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.$\frac{6}{3+\sqrt{3}}$

$3-\sqrt{3}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 7

Rationalizing a Denominator

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

01:37

Rationalize the denominato…

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00:46

02:38

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Rationalize each denominat…

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01:46

So we have six over three plus describe it of three. So I noticed that we have this radical in our denominator and we cannot have that, so we need to get rid of it. The only way to do that is the multiply the top and bottom by the denominator is conjugated, so the contract is whenever you have a and in this case, plus B, so the consequence of this would be a minus B. So whenever you Foyle, you'll get a squared minus B squared. It's just easier You have memorized this formula. So confidence are common handy whenever we have a radical in our denominator, because it will help us get rid of that. Because, as you see B will be squared. So most part, it's hard bottom by three minus through three cause you have to change the sign. So it's simple. Find still have six times three, minus 33 on top and on the bottom with her three squared minus. And then Route three squared someone to go ahead and distribute this six on the top, so have 18 run a six Route three and on the bottom will have nine minus three So if we support for the bottom where six panic we divine are denominator and see larger numbers are enumerating, hating. Devoted my specs. This thing and negative six divided by six gives us negative one, but we'll have to write that one there. We'll just have negative square three.

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