Question

Prove that 2 - √3 is an irrational number​

Answer 1

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Let 2-√3 be a rational no.

Hence,

$2 - \sqrt{3} = \frac{a}{b}$

(Here a and b are coprime)

$\sqrt{3} = \frac{a}{b} - 2$

$\sqrt{3 } = \frac{a - 2b}{a}$

=)a-2b/a is a rational no.

=)√3 is also a rational no.

=)But this contradicts the fact.

=)Our assumption is wrong,

Hence,2-√3 is an irrational no.

Hope it helps uh...