Question

सिद्ध करे कि 7√5 एक अपरिमेय संख्या है​

Answer 1

Let's assume that it is a rational number .

So , we can write it as

$7\sqrt{5} = \frac {a}{b}$ _______ ( 1 )

Here , a & b are two co-prime no.s & b is not equal to zero .

Simplify the eqn. ( 1 ) , dividing both sides by 7 , we get

$\sqrt{5} = \frac {a}{7b}$

Here , a & b are integers , so $\frac {a}{7b}$ is a rational number . So , $\sqrt5$ should be a rational number .

But $\sqrt5$ is an irrational number so , it's contradictory . Therefore , $7\sqrt{5}$ is an irrational number .