Question

prove that 2+√5 is irrational number​

Answer 1

Step-by-step explanation:

let us assume that 2+√5 is a rational

2+√5= a/b. (a and b are coprimes having common factor 1)

send 2 to rhs

√5=a/b-2

√5= a-2b/b

here a-2b/b is rational

but this contradicts the fact that √5 is irrational

this contradiction has arisen because of our wrong assumption that2+√5 is rational

therefore, 2+√5 is irrational

HENCE PROVED

hope it is useful

Answer 2

Answer:

Let 2+√5 is a rational number so it can be written in p/q form where p and q are integers.

2+√5=p/q

-> √5=p/q-2

-> √5=p-2q/q

since A and b are integers so p-2q/q is rational and so √5 is rational.

but this contradicts the fact that √5 is irrational.

This contradiction has arise and because of our incorrect option that 2+√5 is rational.

Thus we conclude that 2+√5 is an irrational number