ALL ABOUT IRRATIONAL NUMBERS AND THEIR PROPERTIES
Introduction: Students up to a certain level have to deal with definite numbers. It does not mean that all the numbers that you see have to be whole numbers. Some of them may not have a proper existence but still, people use them. You can call them irrational numbers and they have a wide range of properties. The mathematicians depict these numbers as a ratio of real and rational numbers. In this way, you can find the square and cube roots of all types of numbers. Without this, you will not be able to solve complex equations in higher classes as well.
How to define these numbers?
These are numbers that you cannot show in the term of a fraction. No matter how many times you simplify these numbers, the denominator will never be zero. Another good way to find an irrational number is to divide it. You will see that no matter how many times you divide the decimal part will keep on expanding. It is a non-terminating number whose value you cannot find as a whole. You have to take a recurring value and use it as an estimate. Some of the most common constants such as Pi, e, etc are irrational numbers.
Some common properties:
You have to keep in mind that irrational numbers are real numbers as well. Thus the properties are just like other real numbers that you use. But when you add it with a rational one, the result will always be an irrational one. For example, if you add 3 with Pi, the decimals of the result will also be infinite. You can add the same property with multiplication as well. The only difference is that you cannot add zero in this case. When you multiply an irrational number with zero you are bound to get the answer as zero.
These properties are very common when you find the result of different equations. You can prove them as well if you take the product of various prime numbers. Besides these, there is no guarantee that the LCM of two irrational numbers will exist. However, if you add or multiply two irrational numbers, you may get a rational number. Even though this sounds a bit odd, Mathematicians have proved this theorem. A very common example of this type is the multiplication of two rooted numbers. When you multiply, the root sign will vanish.
Uses of these numbers in daily life?
You cannot say that you use irrational numbers daily. But in some applications, you will find that the properties are similar. For example, when the banks calculate the compound interests, they use this process. The rate of interest that they use may not always be rational. Besides these, the subject of mensuration deals with irrational numbers a lot. Every time you measure the area of an object, you have to use the irrational value of Pi. Students cannot find the square root of these numbers if they are unfamiliar with this chapter.
In engineering Mathematics, you may hear the term ‘Euler’. You have to use this concept while calculating various objects. You have to be familiar with the various theorems as well. There is a specific way to find irrational numbers with square roots. You need to find two numbers that have proper square root values. In between these two pairs, all the square root values will be irrational. The most basic concept that you have to learn is that the square root of a prime number is always irrational. It is not easy to deal with irrational numbers in just one day. You can find many more interesting tips about rational numbers from the Cuemath website.
