Question

prove that 5-√3 is a irrational giveen that √3 is irrational
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Answer 1

$\large{\mathtt{\underbrace{\red{✠\:Required\:Answer\:✠}}}}$

Let's assume that 5 - √3 is rational

So we can write it as 5 - √3 = $\frac{p}{q}$

Where 'a' and 'b' are co - primes and b ≠ 0

=> 5 - √3 = $\frac{p}{q}$

=> 5 - $\frac{p}{q}$ = √3

=> $\frac{5q-p}{q}$ = √3

Here, ${\red{\frac{5q-p}{q}}}$ is rational, and so √3 is rational .

But this contradicts the facts that 'p' and 'q' have no other common factors other than 1 .

So, we conclude that 5 - √3 is irrational .

Hence proved ........

Answer 2

Answer:

Here is your answer mate.