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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
How many irrational numbers are there between the numbers 1 and 25?
Infinitely many. More than all the rational numbers in total.
Why is pi considered as an irrational number?
Johann Heinrich Lambert proved, in the 18th Century that pi is irrational. However, his proof is pretty complicated. Simpler proofs were found later but even they are not simple and, in any case, well beyond the scope of the pathetic browser that we are obliged to use for posting answers. If you are really interested you can try the following link: en.wikipedia.org/wiki/Proof_that_π_is_irrational#Hermite.27s_proof
Is -8.0 rational or irrational?
-8.0 is a rational number. Irrational numbers are things such as numbers that can't be expressed as a fraction in the a/b form. Such numbers that are irrational include pi, square roots of negative numbers, etc.
Is 0 point 7777 an irrational number?
No because 0.7777 can be expressed as a fraction in the form of 7777/10000
What is the value of the irrational square root of 193 that is between what two numbers?
It is between -5,000,000 and 5,000,000. The question is so poorly phrased that it is hard to know where to begin!
First of all, there is a negative square root of 193 and a positive square root of 193.
Suppose you are only interested in the positive square root. The answer could be that it is between 0 and 5,000,000. It is the positive sqrt so it must be greater than 0. Also, the sqrt of 193 will be less than 193 and so definitely less than 5 million. So that answers your question together with a refinement that I have added.
Next. what are the perfect square numbers in the region of 193? 132 = 169 and 142 = 196
That is 132 = 169 < 193 < 196 = 142 so 13 < sqrt(193) < 14.
Is the square root of 47 a irrational or rational number?
The square root of 47 is an irrational number.
No, 156 is a rational number
An irrational number is a number that cannot be expressed as a simple fraction.
Is 4.198 rational or irrational?
4.198 as a terminating decimal is rational.
4.198 = 4198/1000 = 499/500
-2.5 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
What is the history of rational numbers?
The history of rational numbers goes way back to the beginning of historical times. It is believed that knowledge of rational number precedes history but no evidence of this survives today. The earliest evidence is in the Ancient Egyptian document the Kahun Papyrus. Ancient Greeks also worked on rational numbers as a part of their number theory. Euclid's elements dates to around 300 BC. Indian mathematicians also worked on rational numbers. This is documented in different texts but the most important is probably the Sthananga Sutra which dates back to around the second century BC.
What is an irrational number between 9.0 and 9.1?
It is the square root of 9.5 which is an irrational number
Is a set of rational number a sub set of irrational number?
No, they are disjoint sets. Both are subsets of the Real numbers.
How many squares roots does 36 have?
This can be taken as a trick question.
The principal square root of 36 is 6.
-6 times -6 is 36, so the negative square root of 36 is -6.
So depending on the context of the question, 36 either has one square root, or two.
Mathworld.com has a better explanation at
http://mathworld.wolfram.com/SquareRoot.html
I will not try to duplicate it here because of the use of math symbols.
Are there numbers that are both rational and irrational?
No, no number can be both rational and irrational.
Who invented the early theory of irrational numbers?
no one did it s all fake and PS Egypt is illuminati
Is 52 a rational or irrational number?
It is a rational number, because it can be written as a fraction.
composite number as it is divisible by 1, 3, 7, 9, etc
Pi number can ONLY be used for which shape?
Usually a circle but its properties can also be applied to spheres
Are irrational numbers decimals?
Yes. Every whole number can be expressed as a ratio of whole numbers, and any fraction consisting of whole number numerators and denominators are by definition rational. So irrational numbers will be unending non-repeating decimals.
