Articles containing proofs | Irrational numbers
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational. Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence. For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat. Conversely, a decimal expansion that terminates or repeats must be a rational number. These are provable properties of rational numbers and positional number systems, and are not used as definitions in mathematics. Irrational numbers can also be expressed as non-terminating continued fractions and many other ways. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational. (Wikipedia).
What are Irrational Numbers? | Number System | Don't Memorise
Watch this video to know more about Rational numbers, Irrational Numbers, Real Numbers and Number System. To learn more about Irrational Numbers, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=CtRtXoT_
From playlist Irrational Numbers
Irrational Numbers - What are they?
Learn what an irrational number is in this free math video tutorial by Mario's Math Tutoring. 0:07 What is an Irrational Number 0:11 What is an Integer 0:35 Example of a Rational Number 7 1:02 Example of How a Repeating Decimal is Rational 1:26 Example 1 is Square Root of 7 Rational? 1:40
From playlist Algebra 1
Identifying Irrational Numbers #34
practice sorting and identifying irrational numbers
From playlist Common Core Standards - 7th Grade
Determine Rational or Irrational Numbers (Square Roots and Decimals Only)
This video explains how to determine if a given number is rational or irrational.
From playlist Functions
Can an Irrational Number to Irrational Power be Rational?
Solution on Lemma: http://lem.ma/J7 Twitter: https://twitter.com/PavelGrinfeld
From playlist Problems, Paradoxes, and Sophisms
#2 Idenitfying Irrational numbers
An example that helps in identifying irrational numbers and understanding the basic concepts of irrational numbers.
From playlist Middle School This Year
Determine Approximate Values of Square Roots (Irrational Values)
This video explains how to determine what integer values a square root is between. Then it explains how to use a calculator to approximate square roots. http://mathispower4u.com
From playlist Geometry and Measurement
Comparing Irrational Numbers with Radicals
In this video, I show how to order irrational numbers with radicals. More specifically, I go through examples that require you to determine which irrational numbers are between 1 and 4. For the actual practice questions, I go through them without using a calculator. If you found this vide
From playlist PreAlgebra
Algebra 1 Regents August 2014 #01
In these videos, we cover the August 2014 Algebra 1 common core regents you can find the entire playlist here: https://www.youtube.com/playlist?list=PLntYGYK-wJE0joX8gYIxNNVV5sewtbPZu
From playlist Algebra 1 Regents August 2014
Worked example: rational vs. irrational expressions (unknowns) | High School Math | Khan Academy
Sal determines whether expressions with unknown rational/irrational numbers are rational or irrational. Watch the next lesson: https://www.khanacademy.org/math/high-school-math/math2/math2-complex-num/math2-imaginary-num/v/introduction-to-i-and-imaginary-numbers?utm_source=YT&utm_medium=D
From playlist Algebra I | High School Math | Khan Academy
Chebyshev Polynomials via cos(1°)
In this video, we introduce and motivate the Chebyshev polynomials (1st kind) in proving that the cosines of numerous angles must be irrational numbers. No advanced math beyond high school trigonometry is needed to understand this video, which is quite remarkable considering the many real-
From playlist Math
Recognizing rational and irrational numbers (examples) | Algebra I | Khan Academy
Given a bunch of numbers, learn how to tell which are rational and which are irrational. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers/irrational-numbers/e/recognizing-rational-and-irrational-numbers?ut
From playlist Algebra 1 | Get Ready for Grade Level | Khan Academy
Proof that there is an irrational number between any two rational numbers | Algebra I | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers/irrational-numbers/e/recognizing-rational-and-irrational-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Watch the next lesson: https://www.khan
From playlist Algebra I | High School Math | Khan Academy
Math 101 Introduction to Analysis 091115: Basics (Rational Zeroes Theorem)
Definition of algebraic numbers; the root of 2 is algebraic (and not rational); Rational Zeroes theorem; alternate proof that the root of 2 is irrational.
From playlist Course 6: Introduction to Analysis
Introduction to rational and irrational numbers | Algebra I | Khan Academy
Learn what rational and irrational numbers are and how to tell them apart. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/rational-and-irrational-numbers/irrational-numbers/e/recognizing-rational-and-irrational-numbers?utm_source=YT&ut
From playlist Algebra 1 | Get Ready for Grade Level | Khan Academy
Advanced Knowledge Problem of the Week 2-2-17
Let us know if you found this solution 'too' bland!
From playlist Center of Math: Problems of the Week
Algebra 1 Regents June 2014 #13
In this video we look at the sums of rational and irrational numbers
From playlist Algebra 1 Regents June 2014
a problem on irrational square roots
From playlist Common Core Standards - 7th Grade