Question

Given that √ is irrational number. Prove that 5-√3 is irrational number.​

Answer 1

Step-by-step explanation:

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

$= > 5 - \sqrt{3} = \frac{p}{q}$

$= > \sqrt{3} = \frac{5q - p}{q}$

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......

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

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