Question

5-2root 3 prove that irrational

Answer 1

let if possible 5-2√3 be a rational number
then
5-2√3=a/b
√3=a-5b/-2b
or
√3=-a+5b/2b
since a and b are some integer so we can say that -a+5b/2b is a rational number and also √3 is a rational number but this contradict the fact that √3 is a rational number
This contradiction has arisen due to our wrong assumption that 5-2√3 is a rational number
Hence 5-2√3 is a irrational number

proved ☺️