Question

5-2√3 is an irrational no. Prove

Answer 1

Let 5-2√3be rational
now 3 is rational
3-(5-√3){difference of two rational is rational}
√3 (is rational)(but it's wrong)
therefore5-2√3 is irrational

Answer 2

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