Question

1. Prove that 2√3/5 is irrational.​

Answer 1

Answer:

Let it be rational number

therefore it can be written in form of a and b where a and b are co-prime numbers.

2√3=5a/b

5a/b is rational number as it is of the form p/q which is a rational number.

but we know that √3 is irrational number so our assumption is wrong.

2√3/5 is irrational.

Answer 2

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.