Question

Prove that 5 + √3 is an irrational number.​

Answer 1

Answer:

let be assume that 5+√3 is a rational number.

therefore it can be written in the form of p/q

5+√3=p/q

√3=p/q-5

√3=p-5q/q

p-5q/q is a rational number therefore √3 is also a rational number but it is contradict that √3 is irrational there fore our assumption is wrong amd 5+√3 is an irrational number.

Answer 2

Step-by-step explanation:

Let us assume, 5−3 is a rational number

⇒5−3=qp, where p,q∈z,q=0

5−qp=3

⇒q5q−p=3

⇒3 is a rational number ∵q5q−p is rational

but 3 is not a rational number.

This gives us a contradiction.

∴ our assumption that 5−3 is a rational number is wrong

⇒5−3 is an irrational number.