LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

IRRATIONAL NUMBER

**IRRATIONAL NUMBER –**

**A number which when expressed in decimal form is expressible
as a non-terminating and non-repeating decimal, is called an irrational number.**

__Example.1)__ Every non-terminating and non-repeating
decimal is irrational –

** a) 0.202200022002222220020……….is irrational
number**

** b) 0.5333555533335555553355……….is irrational
number**

** c) 0.2122222111112122211112……….is irrational
number**

__Example.2)__ The square root of every non-perfect square
is irrational. It is easy to show that, √2 = 1.4142…….., which is clearly
non-terminating and non-repeating. So, √2 is irrational.

**On calculation, you shall observe that the square root of
every non-perfect square natural number is non-terminating and non-repeating
decimal. So, it is irrational. Thus, each of the following numbers is
irrational – √2, √3, √5, √6, √7, √8,
√10, √11, √12, √13, √14,……………..etc.**

__Example.3)__ The cube roots of non-perfect cubes are
irrational

**Thus ^{3}√2, ^{3}√3,
^{3}√4, ^{3}√5, ^{3}√6, ^{3}√7, ^{3}√9,
^{3}√10, ^{3}√11,………etc. are all irrational.**

__Example.4)__ The value of π is 3.1416…., which is non-terminating and non-repeating,
π is irrational.

**Note that, π is irrational, while 22/7 is rational.**