Question

5-root3 is rational or irrational explanation I want

Answer 1

Assume that 5 -√ 3 is rational. Then it will be of the form a/b where a, b are coprime integers and b not equal to zero.

Now,
5-√3= a/b
on rearranging we get 5-a/b =√3

since 5 and a/b is rational , so their difference will be rational.

Therefore √3 is rational.

But we know that root 3 is irrational.

But this contradicts the fact that √3 is irrational.

Hence 5 -√ 3 is irrational.