What are some Irrational Numbers
What are some Irrational Numbers
We all know that rational and irrational numbers all together are called Real numbers.
What are irrational numbers is the query which has been frequently asked by
students so here is the answer.
Any number ‘n’ is called irrational if it cannot be written in the form of rational number
i.e. in form of p/q, where p & q are integers and q≠0.
Moreover irrational numbers are the numbers which when expressed in the decimal
form are non-terminating and non-repeating.
Eg: 0.13113111311113…. , 0.232232223…… etc are neither terminating, nor
repeating decimal, so they forms a irrational number.
Further If ‘n’ is any positive integer and we observe that
• If it is not a perfect square, then surely square root of ‘n’ is a irrational number
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eg: square root(2), square root(3) is irrational but square root (4) is a rational number.
Always remember that Square root of any prime number is always irrational number.
• If it is not a perfect cube, then also cube root of ‘n’ is irrational number. Eg: cube
root (2) is irrational but cube root (8) is a rational number. Another amazing fact about
irrational number is π is irrational but if we write 22/7, it is a rational number
What are irrational Numbers
Irrational numbers are the numbers which are not rational numbers. In other words
we can say that any number that cannot be expressed in the form of p/q are termed
as irrational numbers.
If any floating point number (that is a number that has an integer part as well as an
decimal part is termed as floating point number.) cannot expressed as the ratio of two
integers that floating point number is termed as irrational numbers.
Let us take some of the examples of Irrational numbers Now if we take the value of “
pi (π ) “ that is π = 3.1415926535897932384626433832795 This value of π is
impossible to express as the simple ratio of two numbers or two integers instead.
Thus the value of π is an irrational number.
Let us take some more examples to clearly get an image about the irrational numbers
Let us take a value 3.2. Now 3.2 is not an irrational number, it is a rational number as
3.2 can be expressed as a ratio of two integers that is
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A square root of every non perfect square is an irrational number and similarly, a
cube root of non-perfect cube is also an example of the irrational number.
When we multiply any two irrational numbers and the result is rational number, then
each of these irrational numbers is called rationalizing factor of the other one.
What are Rational and Irrational Numbers ?
When we deal Rational and Irrational numbers, the first question arise in our mind is
that what are rational and irrational numbers?
Rational numbers are those numbers which can be represented as fraction means
having numerator and denominator and both in integer form. Let’s take some
examples of rational numbers:
1. 5 is a rational number because it has 1 in its denominator and can be written as
2. 2/3 is also a rational number. Now, the next part of the same question i.e. what are
irrational numbers? Irrational numbers are those which can be represented as a
fraction i.e. numbers except rational numbers. They can only be represented as
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