Question

can u prove that underoot 5 is irrational

Answer 1

Hey dear!

Here is yr answer......



Let us assume √5 is rational

let √5 = a/b ( a, b are co-primes)

=> b√5 = a

Squaring on both sides....

=> 5b² = a²

=> a² = 5b²


Here, 5 divides a²

therefore, 5 also divides a ----------(1)

let, a = 5c

by sub. a = 5c in a² = 5b²


=> (5c)² = 5b²

=> 25c² = 5b²

=> 5c² = b²

=> b² = 5c²


Since, 5 divides b²

Therefore, 5 also divides b ------------(2)



From (1) & (2),

we conclude that, a and b are not co-primes!


So, our assumption is false

Therefore, √5 is irrational!


Hope it hlpz...