tion:(i) 2 1 Let us ASSUME 2 1 is RATIONAL.So we can WRITE this number as2 1 = ba ---- (1)Here, a and b are two co-prime numbers and b is not equal to zero.Simplify the equation (1) multiply by 2 both sides, we GET1= ba 2 Now, divide by b, we getb=a 2 or ab = 2 Here, a and b are integers so, ab is a rational number, so 2 should be a rational number.But 2 is a irrational number, so it is contradictory.Therefore, 2 1 is irrational number.(ii) 7 5 Let us assume 7 5 is rational.So, we can write this number as7 5 = ba ---- (1)Here, a and b are two co-prime numbers and b is not equal to zero.Simplify the equation (1) divide by 7 both sides, we get5 = 7ba Here, a and b are integers, so 7ba is a rational number, so 5 should be a rational number.But 5 is a irrational number, so it is contradictory.Therefore, 7 5 is irrational number.(iii) 6+ 2 Let us assume 6+ 2 is rational.So we can write this number as6+ 2 = ba ---- (1)Here, a and b are two co-prime number and b is not equal to zero.Simplify the equation (1) subtract 6 on both sides, we get2 = ba −62 = ba−6b Here, a and b are integers so, ba−6b is a rational number, so 2 should be a rational number.But 2 is a irrational number, so it is contradictory.Therefore, 6+ 2 is irrational number.