# CLASS-9IRRATIONAL 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.