Question

prove that √3 is irrational​

Answer 1

Answer:

√3 =1.732 and it is irrational

Answer 2

Step-by-step explanation:

Let's assume that √3 is rational. i.e

3/√3=m/n3=m/n, where m and n have no common factors.

Multiplying both side by nn and squaring we get.

3n^2==m^2

Since lhs is divisible by 3, rhs should also be divisible by 3. Thus, we can write m as 3p

3n^2=(3p)^2

=> 3n^2=9p^2

=> n2=3p^2

Since rhs is divisible by 3, lhs should also be divisible by 3. Thus nn is divisible by 3.

Both n,mn,m are divisible by 3, contradicting our original assumption that m and n are co-prime.

Thus, 3–√3 is irrational. Hence Proved.