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a. Write each fraction in simplest radical form. b. Use a calculator to find a rational approximation for the given fraction. c. Use a calculator to find a rational approximation for the fraction in simplest form.$\frac{2+\sqrt{3}}{\sqrt{3}}$

a) a) $\frac{2+\sqrt{3}}{\sqrt{3}}= \frac{(2+\sqrt{3})(\sqrt{3})}{\sqrt{3}(\sqrt{3})} =\frac{2 \sqrt{3}+3}{3}$b) Using calculator: $\frac{2+\sqrt{3}}{\sqrt{3}}=2 \cdot 154700$c) Using calculator: $\frac{2 \sqrt{3}+3}{3}=2.154700$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 7

Rationalizing a Denominator

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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a. Write each fraction in …

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Rationalize the denominato…

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Use rational expressions t…

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Give each answer in simple…

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a. Simplify $\frac{\sqrt{2…

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Find a decimal approximati…

01:32

To rationalize the denomin…

Use rational exponents to …

So first we have on part A. We want to write this in the simplest radical Ford. So we have two plus good of three over this word of three. But we need to get rid of this radical in our nominated. So we need the most part. It's hopping bottom by that same radical, so we'll get to plus route three. So I was really three all over and the square root of three times Spirit of three would just give us three. So if we distribute our square root will have 23 plus and a squared or three times square root of three, just three all over three. And now we bring it in. Simplest radical form, part B. They want us to use a calculator to find a rational approximation for the given fraction. So the given fraction is the original fraction here. So we wanna plug two plus Route three all over route three into our calculators, and we'll get two 0.1 God in part C. They want us to plug in the simplest form. So we're gonna plug in to Route three plus three all over three and sore calculators. And when you do that, we'll get 2.1 bar front. So this was just system so that when you read it in its simplest form, it's still the same infraction. But because we don't want a radical in our denominator, we just have to make some changes to that fraction. And it also shows that whenever you multiply by the radical here, that's just one. So we didn't really change to practice little we just when it we didn't change the value of the fraction. That's a moment to say. We never changed the value of the fracture, and we just multiply or divide so that we can not have a radical in our denominator.

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