Question

Prove that 4-3√2 is irrational?


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Answer 1

Answer:

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. ⇒ 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.