Question

Prove that 5+√3 is irrational​

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

Answer:

ration number can be expressed in the form of p/q

let us assume that 5+_/3 is a rational number

therefore

5+_/3=p/q

_/3=(p-5q)/q

We see that LHS is an irrational number and RHS is rational, which is not possible.

therefore our assumption is wrong and 5+_/3 is an irrational number.

Hope it helps