Question

1) Show that V5 is an irrational number.​

Answer 1

Answer:

Step-by-step explanation:

let's assume √5 is a rational number,

√5=p/q

on squaring,

5=p²/q²

⇒5q²=p² _____1

⇒5 is a factor of q²

⇒5 is a factor of q

let m be an integer that,

p=5m

on squaring,

p²=25m²

by 1,

5q²=25m²

⇒q²=5m²

⇒5 is a factor of q²

⇒5 is a factor of q

this contradicts our assumption as p and q must be co-prime but here they have a common factor.

∴ √5 is an irrational number.