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In $3-14,$ determine whether each of the numbers is rational or irrational.$$2 \frac{1}{3}+\sqrt{3}$$

irrational

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Chapter 3

REAL NUMBERS AND RADICALS

Section 1

The Real Numbers and Absolute Value

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $3-14,$ determine wheth…

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01:38

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all right. Hey, guys. So in this problem, we are given two and 1/3 plus square root three and were asked, determine if this is rational or irrational. And so first, what we're going to do is we see that this involves the sum of two numbers. And since we already know some things about something rational and irrational numbers, we're gonna classify each of these individual components of some as rational or irrational and then decide whether the sum is irrational, rational. So first step let's take a look at each of the components in the sum to 1/3 to 1/3 is equal to 2.3 repeat, and 2.3 repeat is a repeating. It is a repeating decimal, and it could also be written as a fraction. So we know that this number is a rational number. However, when we take a look at square root three square with three equals 1.73 blah blah, blah blah. It's an infinite number that's non repeating, and we know that this is an irrational number. So basically, in this, some were summing a rational, so we're basically something irrational, plus and irrational and from our previous problems. We know for a fact that whenever you some of rational and an irrational number, you are going to get an irrational value. That's just a fact and big due to this fact. We can determine that two on 1/3 plus square root three is indeed gives us an irrational value. Thanks for listening, guys. And I hope this helps office problem.

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