Question: prove that 5-√3 is an irrational number given that root 3 is irrational?
Answer: let us assum that 5-√3 is rational number so we can find two integers a , b. Where a and b are two co - primes number. So it arise contradiction due to our wrong assumption that 5 - √3 is rational number. Hence, 5 -√3 is irrational number.