Question

to prove 5 + root 3 is irrational​

Answer 1

Answer:

let us assume that 5+ root 3 is rational no in the form p/q where q is not equal to 0

5+root 3=p/q

root 3=p/q-5

root 3=p-5q/q

Therefore root 3 is irrational and p-5q/q is rational.

our assumption is wrong hence 5+root 3 is irrational....

Answer 2

Given

A no 5+√3

To find

it is an irrational no

Proof

Let 5+√3 is a rational no than it exis in $\frac{p}{q}$

$\implies\frac{p}{q}$=5+√3

$\implies\frac{p}{q}$-1=√3

Here if $\implies\frac{p}{q}$-1 is a rational than ,√3 is also rational

But we know that √3 is irrational no.

Proved

Therefore,this contradict that 5+√3 is rational

Hence,5+√3 is irrational