Question

prove that 5-root3 is irrational ​

Answer 1

Answer:

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

⇒5−√3​=p/q​

⇒√3​= 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−√3  is irrational

Answer 2

Proof :

5 - √3 is now rational

Because it can be write in the form of $\frac{p}{q}$

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

Hence √3 is irrational.

So ( 5 _ √3 ) become

irrational

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