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Irrational Numbers
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. While their existence was once kept secret from the public for philosophical reasons, they are now well accepted, yet still surprisingly hard to prove on an individual basis. Please post all questions about irrational numbers, including the famous examples of π, e, and √2, into this category.
3,962 Questions
Are rational numbers national numbers?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All natural and whole numbers are rational.
What is the square root of 670?
The square root of 670 is approximately 25.88435821. It is between the squares of 25 and 26.
Are irrational numbers negative integers?
No. Every integer, whether negative or positive, is rational.
How are irrational numbers used?
Irrational numbers can not be expressed as fractions whereas rational numbers can be expressed as fractions
Are all real numbers can be irrational numbers?
No.
Square root of (2, or 3, or 5, or 6, or 7, or 8, or 10, or 11) are all real and irrational.
Why is the square root of 36 rational?
It is because 6 is one of the rational numbers, which are anything ranging from negative numbers, positive numbers, ratios, fractions and decimals, and repeating decimals.
How many irrational numbers are there between 1 and 2?
Infinitely many. In fact, there are more irrational numbers between 1 and 2 as there are rational numbers - in total.
The cardinality of this set is Aleph-0ne.
Is two over three a rational number?
Two over three can be expressed as a ratio (2/3), so it is therefore a rational number.
Is 1.24562 an irrational number?
No because like all rational numbers it can be expressed as a fraction
They are numerical solutions where the number cannot be expressed in the form of a ratio of two integers.
88 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
What are the subsets of irrational numbers?
There are no subsets of irrational numbers. There are subsets of rational numbers, however.
Is 0.91 a rational number or an irrational number or an integer?
It can be written as a fraction, so it is rational.
The difference between two different irrational numbers?
The difference can be rational or irrational.
5 + sqrt(3) and 2 + sqrt(3) are both irrational numbers but their difference is
[5 + sqrt(3)] - [2 + sqrt(3)] = 3, which is rational.
Is the set of irrational numbers closed under division?
No, it is not.
Root2 and root 8 are each irrational. Root8 / root2 =2.
2 is not a member of the set.
