Question

Prove that 3√2 is irrational.​

Answer 1

Let us assume, to the contrary, that 32 is 

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

32=ba

⇒ 2=3ba

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

This contradicts the fact that 2 is irrational. 

So, our assumption is not correct.

Hence, 32 is an irrational number.

Answer 2

Answer:

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➽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..