Question

prove that 2 + root 5 is an irrational number​

Answer 1

Heya mate!!

Here is the answer to your question!!!

Your question :

Prove that 2+√5 is an irrational number.

Solution :

Let us assume 2+√5 as a rational number such that

2+√5 = p/q [ where p and q are integers and q ≠ 0 ]

So 2 +√5 = p/q

√5 = p/q -2 = p -2q /q

Since p, q and -2 are integers and q ≠0

So, p -2q/q is a rational number.

So √5 will also be a rational number.

But we know that √5 is an irrational number.

This Contradiction arisen die to our wrong assumption.

Therefore 2+√5 cannot be a rational number.

Hece: 2+√5 is an irrational number. [ Proved]

Hope it helped!!!