Prove that 2/5√3 is irrational

We can prove that 2/5√3 is irrational by proof by contradiction. Assume for the sake of contradiction that 2/5√3 is rational. This means it can be expressed as a fraction in its simplest form, where the numerator and denominator have no common factors other than 1. Let's call this fraction a/b, where a and b are integers. Multiplying both sides of the equation by 5√3, we get: 2 = (a/b) * 5√3 2√3 = a/b This equation implies that a is a multiple of √3. However, if a is a multiple of √3, then it cannot be in its simplest form with a denominator of b, contradicting our initial assumption. Therefore, our initial assumption that 2/5√3 is rational must be false. Hence, 2/5√3 is irrational.

Prove that 2/5√3 is irrational