Question

prove that 5 + 2√3 is irrational​

Answer 1

Let if possible suppose 5 + 2√3 is a rational number

=> ( 5 + 2√3 ) - 5 is also a rational number

( +5 and -5 cancels and difference of two rational number is also a rational number )

=> 2√3 is also a rational number

=> ( 2√3 ) / 2 is also a rational number

=> √3 is a rational number

which contradicts the fact that √3 is an irrational number...Hence our assumption was wrong. Thus 5 + 2√3 is an irrational number