Question

prove that √3 is irrational....... ​

Answer 1

ok this problem is easy to do

Answer 2

A N S W E R :

• Let √3 be a rational number in the form of a/b, where b ≠ 0.

• Co-prime (a, b) = 1

By squaring both the sides we get :

→ (√3)² = (a/b)²

→ 3 = a²/b²

→ 3b² = a² ......[Equation (i)]

⛬ 3 is factor of a.

Let us take a = 3c, for any integer c squaring both the sides we get :

→ a² = 3c²

→ 3b² = 3 × 3c² .....[From equation (i)]

→ b² = 3c²

⛬ 3 is factor of b.

⛬ 3 is the factor of both a and b.but this contradicts our assumption that co prime of a,b is 1.

⛬ Our assumption was wrong .

⛬ √3 is irrational number.