Question

prove that 3√2 is irrational​

Answer 1

Answer: 3+√2 = a/b ,where a and b are integers and b is not equal to zero .. therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers.. ... So, it concludes that 3+√2 is irrational..

Answer 2

Answer:

Let us assume, to the contrary, that 3  √2

 is  rational. Then, there exist co-prime positive integers a and b such that

3  √2=a/b

  √2=a/3b

√2is a rational  ...[∵3,a and b are integers∴ a/3b is a rational number]

This contradicts the fact that  √2 is irrational.  

So, our assumption is not correct.

Hence, 3  √2  is an irrational number.

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