Question

prove that 2+root 3 by 5 is an irrational number.

Answer 1

Answer:

Let 2root 3 / 5 be a rational no. in the form a/b where, a and b are integers.

Now,

2root3 / 5 = a / b

2root3 = 5a / b

root3 = 5a / 2b

Here. since a/b is a rational no., so 5a / 2b is also a rational no.

Hereby, root3 should also be a rational no.

 

But this contradicts tha fact that root3 is a rational no.

So, our assumption is wrong and hence 2root3 / 5 is an irrational no