Question

Show that (4 + 3√2) is irrational.

Answer 1

Let (4+3√2) be a rational number. 

Then both (4+3√2) and 4 are rational. 

⇒ (4+3√2 – 4) = 3√2 = rational [∵Difference of two rational numbers is rational] 

⇒ 3√2 is rational. 

⇒ \(\frac{1}3\) (3√2) is rational. [∵ Product of two rational numbers is rational] 

⇒ √2 is rational. 

This contradicts the fact that √2 is irrational (when 2 is prime, √2 is irrational) 

Hence, (4 + 3√2 ) is irrational.