Question

सिद्ध करे कि 3 रूट 2 एक अपरिमेय संख्या है​

Answer 1

Answer:

Let us assume, to the contrary, that 3

2

is

rational. Then, there exist co-prime positive integers a and b such that

3

2

=

b

a

⇒

2

=

3b

a

⇒

2

is rational ...[∵3,a and b are integers∴

3b

a

is a rational number]

This contradicts the fact that

2

is irrational.

So, our assumption is not correct.

Hence, 3

2

is an irrational number.