Prove that 5+3 root 2 is an irrational number

Answers (1)

To prove (5+3sqrt2) to be irrational.
First let's assume that it is a rational number,
(5+3sqrt2)=fracab,where a and b are integers.
Rightarrow 3sqrt2=fracab-5
Rightarrow 3sqrt2=fracab-frac5bb
Rightarrow sqrt2=fraca-5b3b  
Since RHS is rational	herefore sqrt2 will be rational too
But according to our own knowledge,sqrt2 is irrational.
There is contradiction,so,5+3sqrt2 is an irrational number.

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