# Given that root 2 is irrational prove that 5+3root2 is an irrational number

Given: √2 is irrational

Now,let us assume that 5 +3√2 is rational

So,

5+3√2 = a/b

3√2 = a/b-5 =a-5b/b

√2 = a-5b/3b

But we know that √2 is irrational

So, our assumption was wrong.

Hence 5+3√2 is irrational.

Hence proved

Regards

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