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Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.$\frac{7+\sqrt{5}}{7-\sqrt{5}}$

$\frac{27+7 \sqrt{5}}{22}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 7

Rationalizing a Denominator

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

02:02

Rationalize the denominato…

01:07

01:35

01:03

00:40

Rationalize each denominat…

01:46

00:57

01:48

02:22

this is number 30. So you have seven plus street five over seven, minus three pots. So because we have this square root and the denominator, we need to get rid of that. And the only way to do that is to multiply. That's hopping bottom by the conjugated. So in this case, we have a minus. B, so it's contra get would be using the same terms, but we need to train just on in the middle, so I'm gonna have a plus B, and whenever we foil this out will have a squared minus and then B squared. It's easier if you would just memorized the formula so you don't have toe Boyle and expand everything. Formula would just make the problem solving go by quicker. So when will it's probably talking bottom by seven plus route drive over seven plus Rupa so have seven plus route by time. Seven place Route five and on the bottom will have seven squared minus five squared. So if you boil, this harp will have seven times seven gives us 49 most bloody used to seven route five animals apart. These two will have seven Route five and then most party soon after. Give this spot. You're on the bottom seven. Square gives us 49 and scared about some scary father spot. It'll be simple by this. Further, I'm gonna combined this 49 our five. What an hour plus five gives us 54. And because we have the same based here and here, we can combine their coefficients of seven. So seven plus seven gives us 14 the 54 plus 14 roots all over. But you know, minus five gives us 44th so they can go over the greatest common factor between these three numbers. Let's start out with two. So 54 divided about two. That would give us 27. Forcing about about two gives a seven and 44 divided by two. Gives us 22 and that's this forest.

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