Question

2-3√5 prove that it is an irrational number​

Answer 1

Step-by-step explanation:

let suppose that 2-3√5 is rational no.

so, 2-3√5=p/q(where p and q Are co prime integers and ,q and p r

not equal to 0)

2-3√5=p/q

-3√5=p/q-2

√5=p/q-2-1/3

√5=3p-6q-q/3q

here,3p,-6q,-q,3q r integers

and every integer is a rational no. so

3p-6q-q/3q is a rational no.but √5 is irrational

and this is not possible that rational=irrational

contradiction occurs,

our supposition is wrong.

therefore 2-3√5is irrational