Question

Prove that √5 is an irrational number

Answer 1

Step-by-step explanation:

Say, √5 is a rational number. ∴ It can be expressed in the form p/q where p,q are co-prime integers. ... Therefore, p/q is not a rational number. This proves that √5 is an irrational number

Answer 2

Answer:

Step-by-step explanation:

Assume that√5 is a rational number

√5= p/q, where p and q have no common factors and q≠0

squaring both sides,

5= p²/q²

p²= 5 q²

5 divides p²⇒ 5 divides p

let p= 5m ( where m is a positive integer)

squaring both sided⇒ p²= 25m²

since p²= 5q² and p²= 25m²

5q²= 25m²

q²= 5m²

5 divides q²⇒ 5 divides q

5 is a common factor of p and q

This is a contradiction to the fact that p and q have no common factors

So, our assumption is wrong

∴√5 is an irrational number