Prove that root 5 is irrational.
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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
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