Question

Prove that root 5 is irrational.​

Answer 1

Answer:

root 5 is irrational

Step-by-step explanation:

• let us assume that root 5 is rational
• root 5 = a/b
• a,b are co primes
• squaring on both sides
• 5=a²/b²
• 5b²=a²
• so 5 divides a(a²)
• let c be some integer
• 5c=a
• squaring on both sides
• 25c²=a²
• substuting 1st equation
• 25c²=5b²
• 5c²=b²
• so 5 divides b(b²)
• so a,b have 5 as their common factor
• but this contradicts the fact that a,b are co primes
• so our assumption is wrong
• therefore root 5 is irrational