Question

show that 5-√13 is irrational​

Answer 1

Answer:

a rational number is always in the form of p/q where q is not equal to 0

Answer 2

Let us assume , to the contrary , that 5 - root 3 is rational.

There exists co - prime integers , a and b ( b is not equals to 0) such that

5 - root 3 = a/ b

Therefore, 5 - a/b = root 3

Rearranging thos equation , we get root 3 = 5 -a/b = 5b - a/b

Since a and b are integers , we get 5 - a/b is rational , and so root 3 is rational .

But this contradictsthe fact that root 3 is irrational .

This contradiction has arisen because of our incorrect assumption that 5 - root 3 is rational

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

This is your answer . I hope it's helpful to you.