Question

proove that5-2√3is an irrational number

Answer 1

we will prove this question by contradiction method.
let 5 - 2 root 3 be a rational no.,
and if x is denoted by rational no then
5 - 2 root 3= x
-2√3=x-5. ( subtraction of two rational number is also rational number)
√3 = -x+5/2 ( division of two rational number is also a rational number)

But now RHS is rational number and LHS is irrational number so LHS is not equal to RHS.
so it contradicts our statement
therefore 5 - 2 root 3 is a irrational number.

hope it helps☺️☺️