Question

show that 5+3 is an irrational number​

Answer 1

Step-by-step explanation:

Let us assume that 5 - √3 is a rational

We can find co prime a & b ( b≠ 0 )such that

5 - √3 = a/b

Therefore 5 - a/b = √3

So we get 5b -a/b = √3

Since a & b are integers, we get 5b -a/b is rational,

and so √3 is rational.

But √3 is an irrational number

Let us assume that 5 - √3 is a rational

We can find co prime a & b ( b≠ 0 )such that

∴ 5 - √3 = √3 = a/b

Therefore 5 - a/b = √3

So we get 5b -a/b = √3 Since a & b are integers, we get 5b -a/b is rational, and so √3 is rational.

But √3 is an irrational number Which contradicts our statement ∴ 5 - √3 is irrational