Question

Prove that √2+3√5 is irrational number

Answer 1

let √2+3√5 is a rational number.
:√2+3√5 = p/q (where p and q are co-prime numbers and q is not equals to 0.)
so,√2+√5= p/3q.....
and as we know that √2 and √5 are irrational numbers, so √2+√5 is also an irrational number and as p, 3 and q are rational numbers. so, p/3q is also a rational number.
and a rational number is not equals to an irrational number...
it happens due to contradiction... hence, our supposition was wrong that √2+3√5 is a rational number. So, it Is an irrational number..