Question

prove 5-√3 is irrational plz give complete ans well explained plz spam=report​

Answer 1

Step-by-step explanation:

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

⇒5−3=qp

⇒3=q5q−p

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

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 ✔️

Hopes it helps u ❤