Question

show that 5-√3 is irrational.

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Answer 1

$Suppose \: that \: 5 - \sqrt{3} \: is \: a \: rational \: number$

$5 - \sqrt{3} = a(a \: belongs \: to \: Q)$

$\sqrt{3} = a + 5$

$Q =Q'$

But Q' is not equal to Q

Therefore our supposition is wrong and

$5 - \sqrt{3}$ is an irrational number