Question

Show that 3√ 2 is irrational​

Answer 1

4.24264069....

the decimal expansion of 3√2 is non-terminating and non-recurring so it is irrational

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Answer 2

Answer:

Let us assume to the contrary that 3√2 is rational

there fore

3√2 = a/b

√2 = a/3b

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

This contradict the fact that √2 is irrational

Hence 3√2 is an irrational number