Question

3. Prove that 3
$\sqrt{2}$
is irrational.​

Answer 1

Answer:

In this case,

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.

Hope this helps.

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