Question

1. Prove that 15 is irrational.
2. Prove that 3 + 2V5 is irrational.​

Answer 1

2.Let us assume that 3+2√5 is rational

so,3+2√5may be written as

3+2√5 =p/q,where p and q are integers,having no common factor except 1 and q isn't=0

2√5=p/q-3

2√5=p-3q/q

√5=p-3q/2q

since p-3q/2q is a rational number as p and q are integers

therefore √5 is also a rational number which is a contradiction.

Thus, our assumption is wrong.

Hence, 3+2√5 is an irrational number.