What are the 3 irrational #s and 3 not real numbers

To answer your question, let's start by understanding the definitions of irrational numbers and not real numbers.

1. Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers (non-zero denominators) and do not terminate or repeat in decimal form. They are endless and non-repeating. For example, the square root of 2 (√2), the value of π (pi), and Euler's number (e) are three common examples of irrational numbers.

To confirm that these numbers are irrational, you can use algebraic proofs. For example, to show that √2 is irrational, you can assume it can be expressed as a fraction, square both sides, and arrive at a contradiction.

2. Not real numbers: These are numbers that cannot be represented on the real number line. They include complex numbers, which are made up of a real part and an imaginary part. The imaginary unit, denoted as "i," represents the square root of -1. Complex numbers are typically written in the form of a + bi, where a represents the real part and bi represents the imaginary part.

Here are three examples of not real numbers:

a) 3i: This is a purely imaginary number with no real part. It represents a point on the imaginary axis.

b) -7 + 4i: This is a complex number with both a real part (-7) and an imaginary part (4i).

c) i: This is the imaginary unit, representing the square root of -1. It has no real part (0 + 1i or simply 1i).

To confirm that these numbers are not real, you can check whether the imaginary part is non-zero.

Remember, these explanations provide a basic understanding of irrational and not real numbers. Further exploration of these topics will help you grasp their properties and applications.