Question

show that 5-√3 is irrational​

Answer 1

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Let us assume the given number be rational and we will write the given number in p/q form

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⇒ $\sf{5\:-\:\sqrt{3}\:=\:\frac{p}{q}}$

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⇒ $\sf{\sqrt{3}\:=\:\frac{5q\:-\:p}{q}}$

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We observe that LHS is irrational and RHS is rational, which is not possible. 

This is contradiction. 

Hence our assumption that given number is rational is false 

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⇒ $\sf{5\:-\:\sqrt{3}}$  is irrational 

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