# Prove that 5+3 root 2 is an irrational number

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

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