Question

Prove √2 is irrational
Solve the problem plz ​

Answer 1

Answer:

hope it helps u.......

see the above image

Answer 2

Step-by-step explanation:

If possible, let √2 =p/q, where p€ Z , q ≠ 0 and p and q have no common factor.

(√2)² = (p)²/(q)². {Squaring both sides)

Therefore 2 = p²/q²

=> p²= 2q² (eqn - 1)

=>2 is a factor of p².

Therefore p² is divisible by 2

=> p is also divisible by 2.

Let p = 2m , where m € Z.

Therefore, p² = 4 m² (eqn - 2)

=> [Putting (eqn - 2) into (eqn-1)]

=> 4m² =2q²

=> 4m²/2 = q²

=> 2m² = q²

=> 2 is a factor of q²

Let q = 2n, where n€Z.

Therefore, √2 = p/q

=> √2 = 2n/2n, which shows that p and q has 2 as common factor

This contradicts our assumption that p and q have no common factor.

Hope It Helps You!