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Prove that the following number is irrational $(2-3 \sqrt{5})$
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$(2-3 \sqrt{5})$
Let us assume that $(2-3 \sqrt{5})$ is rational.
subtract given numbers from 2 , considering 2 is rational number. as we know, difference of two rational numbers is rational
$2-(2-3 \sqrt{5})$ is rational.
$\Rightarrow 3 \sqrt{5}$ is rational
above result is possible if 3 is rational and $\sqrt{5}$ is rational. Because, product of two rational numbers is rational.
but the fact is $\sqrt{5}$ is an irrational.
Our assumption is wrong, and $(2-3 \sqrt{5})$ is irrational
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