Question

prove 5-2root3 is an irrational no​

Answer 1

assume that 5-2 root 3 is rational

5-2 root 3 = a/b , where a and b are integers . 

-2 root 3 = a/b - 5

2 root 3 = 5 - ab 

2 root 3 = 5b/b - a/b

root 3 = 5b - a / 2b

we know that a, b , 2 and 5 are integers and they are also rational 

therefore root 3 will be rational 

but we know that root 3 is irrational

there is a contradiction

so, 5 - 2 root 3 is an irrational number

hope it helps