In the previous post we have discussed about is pi a rational number and In today's session we are going to discuss about list of irrational numbers. Real numbers which are not rational are defined as irrational numbers. We can't write irrational number in an simple fractional form as p/q.It is cannot be written in form of p/q, where p and q are integer and q≠0. The decimal point goes on endlessly without any specific pattern called irrational number.
Example: 1.5 = 3/2 (Rational Number)
∏ = 3.1415926535897….. = ?/? (No ratio, Irrational Number)
The List Of Irrational Numbers consists of number that cannot express in the form of ratio:
List Of Irrational Numbers
|
Present Form
|
∏ (pi)
|
3.14159625358…
|
e (Euler Number)
|
2.71828182459…
|
Ñ°
|
1.61803398874…
|
√2
|
1.41421356237…
|
√3
|
1.73205080756...
|
√5
|
2.23606797749…
|
√7
|
2.64575131106…
|
√11
|
3.31662479035…
|
√13
|
3.60555127546…
|
√17
|
4.12310562562…
|
√19
|
4.35889894354…
|
√23
|
4.79583152331..
|
√29
|
5.38516480713…
|
√31
|
5.56776436283…
|
√37
|
6.08276253029…
|
√41
|
6.40312423743…
|
√43
|
6.55743852430…
|
√47
|
6.85565460040…
|
Listed below are a few facts related to Irrational Numbers:
· If r is Irrational Numbers then –r also Irrational Numbers.
· Irrational Numbers + Rational Numbers = Irrational Numbers
· √2 + 6 = 7.618033988… (Irrational Numbers)
· Irrational Numbers x Rational Numbers= Irrational Numbers
· 3 x √7 = Irrational Numbers
· ∏ x ∏ = Irrational Numbers
· √2 x √2 = Rational Numbers
· √2 + √2 = Irrational Numbers
· √2 - √2 = Rational Numbers
· √2 / √2 = Rational Numbers
The other example of Irrational Number is Uniform Circular Motion. Uniform Circular Motion defines, an object traveling in a circular path at a constant speed. In Uniform Circular Motion a equation related the magnitude of the acceleration of the speed:
Y= 2∏r/T a = 2∏Y/T
Where r is the radius of the path and T is the time taken to make a circle.
So final equation is:
a = Y*Y/r (centripetal equation)
So result from the Uniform Circular Motion is always Irrational.
In Iit Jee Papers some questions also based directly and indirectly on Irrational numbers and Last List Of Irrational Numbers. (know more about list of irrational numbers, here)
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