Question

prove that 7√2÷3 is an irrational number

Answer 1

Theorem 1: The square root of any non-negative integer that is not a perfect square is irrational. 

Theorem 2: The product of a rational number and an irrational number is irrational. 

Theorem 3: The sum of a rational number and an irrational number is irrational. 

 is irrational by Theorem 1. 

 is an integer and therefore rational by definition. 

 is irrational by Theorem 2. 

 is an integer and therefore rational by definition. 

 is irrational by Theorem 3. 

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it