Question

6. Prove that 5 - 2√3 is an irrational number.​

Answer 1

Answer:Let 5-√3 is rational.

Therefore, 5 - √ 3 = a/b(where a and b are coprime).

√ 3 = 5 - a / b

√3=(5b-a)/b

Since a and b are integers, 5b-a/b is rational.

==>√3 is rational.

But, this contradicts the fact that√3 is irrational.

Therefore, our assumption was wrong that 5-√3 is rational.

So, we conclude that 5-√3 is irrational.