Question

prove that 3+√5 is an irrational number​

Answer 1

solution with

Step-by-step explanation:

Let 3 - √5 be a rational number

We can write it as:

3 - √5 = p/q [ where p and q are integer , q ≠ 0 and q and p are co-prime number ]

=> √5 = 3 - p/q

=> √5 = (3q - p)/q

We know that number of form p/q is a rational number.

So, √5 is also a rational number. But we know that √5 is irrational number.

This contradicts our assumption. Therefore, 3 - √5 is an irrational number.