Question

Show that 3√2 is irrational.....

Answer 1

Answer:

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Answer 2

Let 3+√2 is an rational number.

Such that

3+√2 = a/b ,where a and b are integers and b is not equal to zero.

Therefore,

3 + √2 = a/b

√2 = a/b -3

√2 = (3b-a) /b

Therefore, √2 = (3b - a)/b is rational as a, b and 3 are integers..

It means that √2 is rational....

But this contradicts the fact that √2 is irrational..

So, it concludes that 3+√2 is irrational..

hence proved..