Question

3+√2 ek aparimey sankhya he sidh kijiy

Answer 1

We have to prove that , 3+√2 is an irrational number.
But, 1st , let us assume that 3+√2 is a rational number .
therefore, 3+√2 = p/q , where p , q € z , p and q are coprime , and q is not equal to 0.

=> 3q + q√2 = p
=> q√2 = p/3q
=> √2. = p/3q^2

since, p and q , are integers , so p/3q^2 is. a rational number.
But it is not possible , because , √2 is irrational.
therefore , our assumption is wrong.
and , so, 3+ √2 is an irrational number.