An irrational number happens to be one that cannot be expressed in the form of a ratio. Considering another angle a real number that is not a rational number is an irrational number. The discovery of irrational number took place in the 5th century. The sad part was this theory did not have a lot of takers and was dumped. But irrational numbers exist, and if you have an idea about the concept of it things become easy.
The properties of an irrational number
The properties of an irrational number makes it easy for us to understand as you can choose them from a set of real numbers. Let us get to some of the properties of an irrational number
- They consist of non- terminating and non- recurring decimals
- They are an extension of real numbers
- The moment you go on to add a rational and an irrational number together, the sum that emerges is an irrational number only. Coming to an irrational number y and a rational number x the result X+ Y= an irrational number
- The addition, multiplication, division or subtraction of a couple of irrational numbers will not always be a rational number
- When it comes to a couple of irrational numbers, you multiply it by a non- zero rational number, the product would be turning out to be an irrational number.
The process to identify an irrational number
It is an obvious fact that an irrational number turns out to be a real number. It cannot be expressed in the form of p/q and q does not equal to zero. Conversely if any number can be expressed in the form of p/ q and q does not equal to zero it is a classic example of a rational number.
The symbol of irrational numbers
Before knowing the symbols of irrational numbers let us try to understand the symbols of other numbers
- N is for natural numbers
- I for imaginary number
- R for rational number
- Q for rational number
The real numbers is a combination of both rational and irrational numbers.( R-Q) indicates that it is possible to arrive at an irrational number where you deduct rational number from the real number.
Interesting points of rational and irrational numbers
A proper analysis of rational numbers and irrational numbers gives you a proper understanding on why it is part of the real numbers.
- The product of a couple of irrational numbers may turn out to be rational or irrational.
- Coming to the set of an irrational number it would not be closed under the process of multiplication that would be the set of rational number
- The multiplication or addition of a couple of irrational numbers may turn out to be rational.
- It has to be said that rational along with irrational number is not the same. It is necessary that all the numbers have to be represented in the form of p/q which are integers. Here q will not be equal to 0 that would not be a rational number. Another important point to consider is that it is not possible to express irrational number in the form of p/q
- The major difference between rational and irrational numbers is that it would not be terminating and non -repeating. On the other hand an irrational number would repeat and neither terminate after a specific set of decimal points
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