Question

given that √2 is irrational prove that ( 5+3√2 ) is an irrational no. ?

Answer 1

Hope this helps :)
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Answer 2

Let us assume that 5+$3 \sqrt{2}$ is rational.
Then it can be expressed in the form of
      5+3root2=p/q, where p and q are coprime non zero integers.
       3root2=p/q-5

       root2=(p/q - 5)1/3                                   ...........(i)
From (i) we can say that root2 is rational. But this contradicts the fact that root2 is irrational. Hence our assumption is wrong
Therefore 5+3root2 is irrational.