Question

Prove that 2/5- root 5 is irrational...

Answer 1

Answer:

Let 2+√5 a rational.

Step-by-step explanation:

2+√5=p/q

2-p/q=√5

2q-p/q=-√5

as -5 is a rational number.

therefore 2q-p/q is also a rational number

But now-√5 is not a rational

so, our statement is contradictory

hence, 2/5-√5 is an irrational.