Question

Can we prove root 3 + root 5 as irrational number by proving each of them separately as irrational number?

Answer 1

Let us assume that 3+√5 is a rational number

therefor 3+√5 = a ( 'a' is a rational number)

√5 = a - 3 --------(eq. 1)

in eq. 1,

√5 is an irrational number but,

a-3 is a rational number

This is contradictory

Hence we can say that 3+√5 is an irrational number