Question

root 2 is a irrational no. prove in short ​

Answer 1

Answer:

Step-by-step explanation:

since it is under root and does not have any perfect square

so it is irrational

Answer 2

let us assume to the contrary that root2 is rational.

therefore root 2=P/q

p and q are co prime and q not equal to zero

sq. both the sides

p^2 = 2q^2

2 is a factor of p^2

therefore 2 is a factor of p

let p=2c

sq. both sides

4c^2=2q^2

q^2= 2c^2

2 is a factor of q^2 therefore 2 is a factor of q

this contradicts the fact that p and q are coprime

this contradiction has arisen due to a incorrect assumption that root 2 is rational

therefore root 2 is irrational