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Given that $\sqrt{5}$ is an irrational number, prove that $2 + 3\sqrt{5}$ is an irrational number.
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Solution: Let $2 + 3\sqrt{5} = a$, where '$a$' is a rational number
$\Rightarrow \sqrt{5} = \frac{a - 2}{3}$
Here L.H.S. is an irrational number but R.H.S. is a rational number
So, our assumption is wrong
Hence, $2 + 3\sqrt{5}$ is an irrational number
$\Rightarrow \sqrt{5} = \frac{a - 2}{3}$
Here L.H.S. is an irrational number but R.H.S. is a rational number
So, our assumption is wrong
Hence, $2 + 3\sqrt{5}$ is an irrational number