Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all ...

Question

Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Irrational numbers

Accepted Answer

Hello, today we're going to be enumerating all the elements of M that fall within the set of irrational numbers. So what exactly is an irrational number? Well, an irrational number is a number that can be expressed as a continuous decimal. The most famous irrational number is pi pi is equal to 3.141592. And so one, it's a never ending decimal. So pi is considered an irrational number. Another example of an irrational number is the square root of five. The square square root of five can be rewritten as 2.236067. And so one. So what we wanna do is we want to identify all of the integer, all of the irrational numbers inside the set of M that can be rewritten as continuous decimals. And one thing to help us out is that an integer cannot be considered an irrational number. An integer is any number that is expressed as a whole number. So for example, integers include 120, negative three negative five and so one. So what we can go ahead and do is identify all the integers within the set of M and eliminate those integers from the set of M. So the integers that are given to us are negative 13 09 and 19. Since these numbers are classified as integers, they don't fall underneath the set of irrational numbers. So what we need to do now is we need to identify the value of the remaining elements in the set of M. So let's take a look at negative 16, divided by four 16 is divisible by four and negative 16, divided by four can be rewritten as negative four. Negative four is considered an integer and does not fall under the set of irrational numbers. So we can cancel out that element from the set of irrational numbers. Next, let's take a look at negative three divided by 10, negative three divided by 10. When put into a calculator gives us the value of negative 0.3. This is not considered a continuous decimal. So negative three divided by 10 does not fall under the set of irrational numbers. Next, let's check negative square root of 11 when placed into a calculator, negative square root of 11 gives us negative 3.316624 and so on. So negative square root of 11 can be rewritten as a continuous decimal. Therefore, it is considered an irrational number. Next, we'll check the value of two divided by five and two divided by five. When placed into a calculator, gives us the value of 0.4. This is not a continuous decimal. So two divided by five is not an irrational number. Next, we'll check five pie when placed into a calculator. Five. Pi gives us the value of 15.70796. And so on five pi can be rewritten as a continuous decimal. So five pi is an irrational number. And finally, we'll check the value of the square root of 18. When placed into a calculator, the square root of 18 gives us the value of 4.242640 and so on. So the square root of 18 can be rewritten as a continuous decimal. Therefore, it is considered an irrational number. So in the set of M, there are only three numbers that are considered irrational numbers. We have the negative square root of 11 5 pi and the square root of 18. And this is going to be the answer to this problem. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Irrational numbers

Key Concepts

Irrational Numbers

Set Membership and Classification

Simplification of Radicals and Fractions

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